Quizlet Flashcards
in force premium
full term premium for policies that are in effect at a given point in time
reported losses
paid losses + case reserves
estimated ultimate losses formula
reported losses + ibnr reserve + ibner reserve
operating expense ratio formula
uw expense ratio + LAE/earned premium
combined ratio formula
loss ratio + LAE/earned premium + uw expense/written premium
fundamental insurance equation
premium = losses + LAE + uw expenses + uw profit
underwriting guidelines
a set of company-specific criteria that can affect decisions of whether to accept a risk or can alter aspects of the premium calculation
what do underwriting guidelines specify
decision to accept risk, company placement, tier placement, schedule rating credits/debits
criteria for exposure bases
proportional to expected loss,
practical (can be split up into objective and verifiable), historical precedence
extension of exposures method
rerating every policy to restate the historical premium to the amount that would be charged under the current rates
case incurred loss
reported loss
classification ratemaking
the process of grouping risks with similar loss potential and charging different manual rates to reflect differences in loss potential among the groups
first stage of classification ratemaking
determining which risk criteria effectively segment risks into groups with similar expected loss experience. usually different levels of a rating variable
second stage of classification ratemaking
calculates the indicated rate differential relative to the base level for each level being priced
adverse selection
when failure to accurately price individual risks results in a company having a disproportionally high amount of high risk policy holders
4 categories of risk classification criteria
1.statistical
2.operational
3. social
4. legal
3 important factors for statistical classification criteria
- statistical significance
- homogeneity
- credibility
4 important factors for operational classification criteria
- objectivity
- cost to administer
- verifiability
- constancy
4 important factors for social classification criteria
- affordability
- causality
- controllability
- privacy concerns
primary shortcoming of univariate rate classification methods
they do not take into account the effect of other rating variables
main benefit of multivariate rate classification methods
they consider all rating variables simultaneously
overall benefits of multivariate rate classification methods
they consider all rating variables simultaneously, they remove unsystematic effects in the data (noise), they produce model diagnostics (additional information about the certainty of results and the appropriateness of the model fitted), and they allow consideration of the interaction, or
interdependency, between two or more rating variables
According to “The Practitioner’s Guide to Generalized Linear Models” standard errors are:
an indicator of the speed with which the log-likelihood falls from the maximum given a change in parameter
2 common statistical diagnostics
- standard errors
- measures of deviance
a deviance
a single figure measure of how much the fitted values differ from the observations
factor analysis
a data mining technique to reduce the number of parameter estimates in a classification analysis. This can imply a reduction in the number of variables or a reduction in the levels within a variable.
cluster analysis
Data mining technique that seeks to combine small groups of similar risks into larger homogeneous categories or “clusters.”
when is cluster analysis most commonly used
when rating for geography
data mining techniques can enhance a ratemaking exercise by:
- whittling down a long list of potential explanatory variables to a more manageable list
- providing guidance in how to categorize discrete variables
- reducing the dimension of multi-level discrete variables
neural network
gathers test data and invokes training algorithms designed to automatically learn the structure of the data. This technique has been described as a recursion applied to a GLM.
*Its a data mining tehnique
challenges to territorial ratemaking
geography tends to be highly correlated with other rating factors, and the data in each individual territory may be sparse
high-dimensionality
a challenge for territorial ratemaking in which data in individual territories is sparse
2 phases to territorial ratemaking
- establishing territorial boundaries
- determining rate relativities for the territories
first step of establishing territorial boundaries
determining the basic geographic unit
second step of establishing territorial boundaries
estimate the geographic risk of the territory by isolating the geographic symbol in the data
spatial smoothing
since geographic risk tends to be similar for units in close proximity, smoothing improves the estimate of any individual unit by using information from nearby units
2 types of spatial smoothing
- distance-based
- adjacency based
distance-based spatial smoothing
weighting the information from one geographic unit with the information from all nearby geographic units based on the distance from the primary unit and some measure of credibility
advantage of distance based smoothing
easy to understand and implement
disadvantage of distance based smoothing
the assumption that a certain distance has the same impact on similarity of risk regardless of whether it is an urban or rural area.
Additionally, the presence of a natural or artificial boundary between two geographic units is not taken into consideration
adjacency based spatial smoothing
weights the information from one geographic unit with the information estimators of rings of adjacent units
advantage of adjacency based smoothing
it handles urban/rural differences more appropriately, and accounts for natural or artificial boundaries better than the distance-based smoothing
adjacency-based smoothing tends to be most appropriate for which perils
perils driven heavily by socio-demographic characteristics
dangers of over-smoothing
the actuary may be masking the real spatial variation among the risks
dangers of under-smoothing
the actuary may be leaving considerable noise in the estimator
what is the goal when combining units into territories
minimize within territory heterogeneity and maximize between territory heterogeneity
Ward’s clustering method
creates boundaries that lead to the smallest within cluster sum of squares difference. This tends to produce clusters that have the same number of observations.
formula for limited average severity
LAS(H) = integral from 0 to H of(x*f(x)) plus H * the integral from H to infinity of(f(x))
increased limit factor formula
LAS(H)/LAS(B)
loss elimination ratio
the rate by which losses and expenses are reduced as a result of an increase in deductible
what approach do commercial lines insurers typically use to determine applicable expense provisions
the all variable approach
coinsurance clause
the insurer may require a minimum insurance to value or else payment on covered losses will be reduced proportionately by the amount of underinsurance
coinsurance apportionment ratio
the relationship between the amount of insurance selected and the coinsurance requirement and is the factor applied to the loss amount to calculate the indemnity payment
formula for coinsurance apportionment ratio
coinsurance apportionment ratio: a = face value of policy/(coinsurance percentage * value of property)
coinsurance penalty
the amount by which the indemnity payment is reduced by the application of the coinsurance clause
3 conditions for a coinsurance penalty
- A non-zero loss has occurred (i.e., L > 0).
- The face amount of insurance is less than the coinsurance requirement (i.e., F < cV).
- The loss is less than the coinsurance requirement (i.e., L < cV).
guaranteed replacement cost
a policy feature that allows replacement cost to exceed the policy limit if the property is 100% insured to value and, in some cases, subject to annual indexation.
classical credibility estimate
estimate=(zobserved experience)+((1-z)related experience)
buhlmann credibility estimate
estimate=(zobserved experience)+((1-z)prior mean).
where z = least squares version
in least squares credibility what is the formula for Z
N/(N+(E(Var(x))/Var(E(x))
hard market
the phase of the underwriting cycle that sees higher price levels and increased profitability
variable premium
the portion of the total premium that varies by risk characteristics
flat or additive premium
the portion of premium that is derived from expense fees or other dollar additives
formula for proposed fixed expense fee
FE/(1-V-Q)
proposed base rate with flat premium components
Bp = Bc x (Pp-Ap)/(Pc-Ac)
Formula : proposed base rate under weighted average rate differential method
Proposed base rate = (proposed average premium - proposed additive fees) / proposed average rating factor
off-balance factor
1/(1+% change in average rate differential)
what to do when rates increase as a result of a minimum premium
multiply the base rate by the offset factor = (prem without min)/(prem with min)
premium transition rule
dictates the minimum or maximum amount that a premium can change for a single insured in one renewal
ex ante moral hazard
occurs when there is an increase in the underlying risky behavior causing the loss
ex post moral hazard
occurs when an individual asks the insurer to pay for more of the negative consequences than would have otherwise been the case
2 methods of aggregating exposures
- calendar year exposures
- policy year exposures
which exposure aggregation method can assign a single earned exposure to multiple time periods
calendar year exposures
2 types of manual rate modification techniques
- experience rating
- schedule rating
Primary insurance
to the first layer of insurance coverage. Primary insurance pays compensation in the event of claims arising out of an insured event ahead of any other insurance coverages that the policyholder may have
Umbrella and excess insurance
typically refers to liability types of coverage available to individuals and companies protecting them against claims above and beyond the amounts covered by primary insurance policies or in some circumstances for claims not covered by the primary policies.
5 elements of unpaid claim estimate
- case outstanding
- provision for future development on known claims
- estimate for reopened claims
- provision for claims incurred but not reported
- provision for claims in transit (incurred and reported but not recorded)
TPA
Third Party claims Administrators who handle claims from beginning to end.
IA (Independent Adjuster)
Hired by insurance companies to handle specific claims for which the insurer does not have expertise
First decision of a claims adjuster
whether or not the claim is covered under the terms of a valid policy
Second step for a claims professional
Set up an initial case outstanding
case outstanding
the estimated future payments on a claim at any specific point in time. This includes all expenses
When can the pure premium indication method not be used?
When exposure info is unavailable
When can the Loss Ratio indication method not be used?
When pricing a new line of business because it requires current rate
First trend factor in two step premium trending
factor=(Latest period AWP @ CRL)/(Avg EP @ CRL)
Premium trend length
(average written date during the period the proposed rates are expected to be in effect) - (average written date of the latest period of awp data)
Second trend factor in two step premium trending
factor=(1+%trend)^(Premium trend length)
When is harwayne’s credibility method used?
when the subject experience and the related experience have significantly different distributions
formula for complement of credibility using ILF’s
C=La*(ILF(x+a)-ILFa)/(ILFa). where La=the losses capped at attachment point a (avg Pure premium capped at a). ILFx+a is the increased limit factor of the excess layer (upper boundary)
What is the ILF complement of credibility used for
to adjust losses that are capped at an attachment point to produce an estimate of losses in a specific excess layer
formula for complement of credibility using Lower Limits analysis
C=Ld*(ILF(x+a)-ILFa)/(ILFd). Where Ld=losses capped at some lower limit d
when is lower limits analysis complement of credibility used for?
If the losses capped at the attachment point are too sparse
formula for complement of credibility using Limits analysis. (NOT LOWER LIMITS)
C=LRSum[Pd(ILF(min(d,a+x))-ILF(a))/ILF(d)].
where Pd=Total premiums for policies within limit d.
The sum is for all limits d above a.
complement of credibility for class x using rate change of larger group
C=Loss cost for class x * (1+indicated rate change for larger group).
Cred weight loss costs then calculate the indication.
what are berquist sherman techniques used for
adjusting development triangles for changes in claim settlement rates or case reserve adequacy
The main assumption of the paid Berquist Sherman technique
changes in disposal rates are due to speedups or slowdowns in claim settlement rates and not due to changes in the rate of reporting of claims or changes in prioritization between small and large claims
what is the paid berquist sherman technique used for
adjusting development triangles for changes in claim settlement rates
what is the reported berquist sherman technique used for
adjusting development triangles for changes in case reserve adequacy
The main assumption of the reported Berquist Sherman technique
Any differences between the annual changes in average case reserves at each maturity and the severity trend are due to changes in case reserve adequacy and NOT due to large unpaid losses
Which Berquist Sherman technique needs a severity trend to adjust for inflation
Reported Berquist Sherman Technique
disposal rate
closed claims/projected ultimate claims
How do you adjust each cell of the cumulative paid claim triangle when doing a berquist sherman settlement rate adjustment?
Let X=Paid losses,
D=Disposal Rate,
N=Next Collumn,
S=Selected,
T=This Collumn,
P=Previous Collumn.
Adding: XT+(XN-XT)x[(DST-DT)/(DN-DT)].
Subtracting: XP+(XT-XP)x[(DST-DP)/(DT-DP)]
What determines if berquist sherman case reserve adequacy adjustment is appropriate?
If the trend in average outstanding case reserve is different from the trend in average paid severity
How do you adjust each cell of the incurred loss triangle in the berquist sherman case reserve adequacy adjustment?
Detrend the average case outstanding triangle for the severity trend and multiply by open claims, then add paid losses.
What is the extra necessary step when doing berquist sherman for both claim settlement rates and case reserve adequacy?
you need to calculate the adjusted open claim counts as the reported claim clounts minus the adjusted cumulative closed claim counts (calculated using the selected disposal rates). Then the incurred loss triangle will be (adj open claim counts*adj avg case reserve)+adjusted cum. paid losses
chain ladder method
link ratio method or Development method
when is expected claim ratio loss development commonly used?
When entering a new line of business with insufficient data.
When operational or environmental changes make historical data irrelevent.
Or when estimating ultimates at early maturities for long tailed lines of business where the early age-to-ultimate factors are highly leveraged.
How do you calculate expected ultimate losses using the expected claim ratio method?
Ultimate for AY= expected claim ratio * earned premium for AY.
(- OR -) Ultimate for AY = expected pure premium * earned exposures for AY.
Bornhuetter ferguson development is a credibility weighted average of what two techniques?
The “development” method (Link Ratio) and the expected claims ratio. Z = (1/CDF)
Banktander method
credibility weighted average of “development technique and BF method. Z = (1/CDF)
Cape Cod development method ultimate losses formula
Ultimate = actual reported losses + On level earned premium * Expected Claim Ratio * % Unreported.
Where Expected Claim ratio is:
sum(trended reported losses for relevant AYs)/(sum(on level earned premium * % reported))
The denominator of that expected claim ratio is called the used up premium
formula for coinsurance penalty
e = min(cV,Loss)-min((cV),(Loss)x(a)). a = coinsurance apportionment ratio
formula for revised territorial base rate
new terr base rate = (Loss ratio relativity x territory credibility x base rate) / [weighted avg of (cred x Loss ratio relativity)]
formula for experience rating credit/debit ratio
CD = [(AER-EER)/(EER)] x Z.
AER = Actual experience ratio. EER = Expected experience ratio. Z = credibility.
AER = Experience Ultimate / Company subject basic limit loss.
composite rate
estimated premium / trended exposures
retrospective rating plan
a retrospective rating plan uses the insured’s actual experience during the policy period as the basis for determining the premium for that same period.
basic formula for retrospective premium
retro premium = [Basic premium + (reported losses x loss conversion factor)] x Tax multiplier.
Where the retro premium is subject to a minimum and maximum
formula for basic premium used to calculate retrospective premium
basic premium = [expense allowance - expected loss ratio x (loss conversion factor - 1) + Net insurance charge] x Standard Premium
Formula for net insurance charge (used in retro premium formula)
net insurance charge = [insurance charge - insurance savings] x Expected Loss Ratio x Loss conversion factor
minimum premium allowed in retro premium calc
min prem = minimum retrospective premium ratio x standard premium
When projecting premium, if given quarterly @ crl, use most recent avg qrtrly @ crl to project instead of avg of most recent experience year
multiply latest avg written @ CRL by earned exposures for each experience year and then apply the premium trend factor
when they ask for projected premium @ CRL, they may want a projected value for each experience year given
just so you know (jsyk)
How to apply ulae on exam 5 questions
find average ulae/(loss+ALAE) for the experience years and apply a multiplicative factor to (loss+ALAE) of each experience year
formula for residual indication of latest rate change
residual indication = (1+latest indication)/(1+latest rate change taken)
formula for trended present rates indication
(1+residual indication) x (1+net trend)^(# of years between requested effective date last rate change and current proposed effective date)
Non-modeled cat provision per AIY
(Straight Average of cat loss to AIY ratio of every year given) x (1+ULAE/(Loss & ALAE))
It seems like when selecting AIYs use the average of most recent 2 years of projections
jsyk
is NCOR added to losses before applying variable expense and premium?
yes
When given trends for freq and severity what do you use for a loss trend
(1+freq)x(1+sev)
When using multiple experience years for premium, do you still have to trend historical if you have brought rates to crl?
yes, you have to do both
For CRL calculation: if something affects “all policies in force” treat it like a vertical line in the Parallelogram method
yo
ACTUAL QUESTION: When selecting development factors, describe characteristics for which you should review the claim development experience.
THING: progression of age-to-age factors across dev periods. WHY: the pattern should be decreasing.
THING: Stability of age-to-age factors for the same development period. WHY: Greatest variability in age-to-age factors is at earlier ages.
THING: Low credibility of experience WHY: low claims volume, or organizational changes
THING: Changes in patterns WHY: May suggest changes in internal ops or external environment
THING: Applicability of historical experience WHY: Obvious
When is paid claim development more accurate then reported claim development?
when the company has case outstanding adequacy changes because the LDFs from prior years wil not work for more recent years
DO NOT SAY: when looking at a short tailed coverage
potential problems that may cause an ultimate loss estimate to be inaccurate
widely varying age-to-age development factors for a single collumn, not enough data points, not enough columns used to capture full development
How to check if there has been a strengthening of case reserves
Strong increase in (% increase in average case outstanding) when looking down the collumn of Average Case Outstanding triangle.
frequency severity disposal rate technique
- Set up
a. CPC & IPC triangles
b. CPL & IPL triangles
c. UC values (develop CPC triangle to ult) - Use Disposal rates to project counts
a. CDR triangle then make selections for each dev period
- CDR = CPC / UC
b. Project IPC (lower right portion of IPC triangle)
= (UC - Closed # t) * (Selected DR t+1 - Selected DR t) / ( 1- Selected DR t)
- Project Severities
a. Trended IPS (Incremental Paid Severity) triangle
then make selections
Trended IPS = IPL/ IPC x (1+ trend) ^(Trended year - AY)
b. Calculate final unpaid amounts for each dev period
Unpaid = selected counts from step 2b x selected sev from step 3a
ultimate losses = paid + unpaid
case outstanding development technique 1
1.create a remaining in case ratio triangle where each cell = case outstanding / (case outstanding previous age)
- use that triangle to select ratios for each age
- use the selected ratios to fill in the not fully developed years of the case outstanding triangle, where each previously empty cell = (selected ratio) x previous age case outstanding
- Then create incremental paid on prior case ratio triangle where each cell = (incremental paid loss)/(previous age case outstanding). and make selections for each age
- Use selected ratios from step 4 to fill in the empty cells of the incremental paid loss triangle where each previously empty cell = (selected paid on prior case ratio) x (case outstanding)
- ultimate for a year is the sum of the incremental case row
case outstanding development technique 2
- You are given reported and paid cdfs. Use them to calculate case outstanding development factor = (Ultimate claims - paid claims)/(reported claims - paid claims) = 1+[(ReptCDF - 1)x(Paid CDF)]/[PaidCDF - ReptCDF].
- Unpaid claims for an AY is (latest case outstanding)x(Case outstanding Development factor)
Reason for historical precedence as a criterion for exposure bases.
It is costly to change an existing exposure base since it can result in large premium swings for individual insureds
It is costly to change an existing exposure base since it can result in large premium swings for individual insureds
If its a continuous change: adjust historical premiums using a premium trend. If its a one time change: use parallelogram or extension of exposures to adjust
how do you apply historical trend to premiums in past experience years
(Earned Exposures for the experience year) x (Latest avg written premium @ Crl)
Direct effect and indirect effect of a law change
A direct effect is the direct impact on premium or losses solely due to the law change, not taking into account the human response to a change.
For example, if the maximum benefit is increased, losses will automatically go up for any workers whose benefits were previously capped by the maximum.
An indirect effect is the impact on premium or losses as a result of a change in human behavior caused by the law change.
For example, if the maximum benefit is increased, workers might stay out of work longer or more workers might file claims due to the increased financial incentive. (workers comp example)
formula for excess loss factor
losses in XS of cap = (ground up excess losses-(excess claims)x(individual large loss cap)).
excess loss factor = [(losses in XS of cap)/(reported losses-loss in XS of cap)] + 1
Formula : Adjusted reported losses using an excess loss factor
Adj losses = (reported losses - loss in XS of cap for the year)x(excess loss factor)
Problem with leaving shock losses in the data
You overstate the rate indication after years with shock losses and understate the rate indication
after years with no shock losses.
diagnostics used to test generalized linear models
Standard errors: Narrow standard errors around estimates suggest that a variable in the model is statistically significant.
Deviance tests (such as Chi-Squared or F tests: These tests are used to compare models with different variables in them.
Consistency over time: Estimating parameters on data sets for consecutive time periods allows you see whether the estimates tend to be stable over time. If the results are more stable over time, they tend to be more reliable for future predictions.
Validation using a holdout sample: You can split a data set into a modeling data set and a holdout sample. You then build the model using the modeling data set, and use it to predict values in the holdout data set.
LAS for a layer of losses
LAS((H-B) xs B) = [(Losses in layer)-(# of claims in layer)x(B)+(# of claims above layer)x(H-B)]/(# of claims above B)
Formula : LAS(H) for H higher than some B limit. Used when there is censored data for lower limits.
LAS(H) = LAS(B)+Pr(X>B)xLAS((H-B)xsB).
When Calculating Pr(X>B) dont consider data from losses censored at B.
Describe a difference between using a GLM and a univariate approach using limited average severities
GLMs do not assume that the frequency is the same across all limits, so the GLM results can reflect adverse or favorable selection. This may produce counter-intuitive results such as expected losses decreasing as limits increase.
claims-made policies
policies that require that a claim is reported within the policy period for a payment to be made
5 Claims-Made Ratemaking Principles
- A claims-made policy should always cost less than an occurrence policy as long as claims costs are increasing
2.If there is a sudden unpredictable change in the underlying trends, the claims-made policy priced based on the prior trend will be closer to the correct price than an occurrence policy based on the prior trend
- If there is a sudden unexpected shift in the reporting pattern the cost of a mature claims-made policy will be affected relatively little, if at all, relative to the occurrence policy
- Claims-made policies incur no liability for pure IBNR, so the risk of reserve inadequacy is greatly reduced.
- The investment income earned from claims made policies is substantially less than under occurance policies
What happens when a person switches from a claims-made policy to an occurrence policy?
there will be a gap in coverage for claims that occurred during the claims-made policy term but are reported after the claims-made policy expires. To deal with this gap a claim-made insurer can offer tail coverage.
2nd-year claims-made pure premium for AY
2y CM PP = ((% reported in previous year)+(% reported in this year))(Previous year CM PP)(1+loss trend)
Formula for experience modification
=Zx(Experience rating credit/debit).
so
experience mod=Zx(AER-EER)/(EER)
key advantage of the cape cod method of development
the Expected claim ratio is estimated from historical data instead of being judgmentally selected. Also random fluctuations at early maturities do not significantly distort estimates
tail factor
For some lines of business, the historical data triangle may not reach ultimate. The factor that accounts for any additional development beyond that included in the standard loss development method is referred to as a “tail factor.”
Methods for selecting a tail factor
• Doing a special study that contains more years of data.
• Using an industry benchmark tail factor.
• Fitting a curve (e.g., exponential decay) to the LDFs and extrapolating the tail factor.
• Use reported-to-paid ratios at the latest paid development period.
• Judgment (e.g., arbitrarily picking a value like 1.05).
Difficulty with selecting a tail factor for claims development.
There is generally little relevant data that can be used in the tail. The tail selection is very important because the selection affects all accident years reserve needs, thus has a disproportionate leverage on the total reserve need.
What is the goal of ratemaking?
The goal of ratemaking is to assure that the fundamental insurance equation is appropriately balanced.
When doing calendar year written exposures a cancelled policy is a negative written exposure is equal to
it is equal to -(fraction of policy unearned) exposures
policy year written exposures
Each policy written during the calendar year is worth the fraction of the policy that will eventually be earned. You have to know if it will eventually be cancelled mid way through or not.
Policy year parallelogram method
make the year a parallelogram instead of a square. Then do the areas the same way.
Other acquisition is divided by Written premium to come up with a percentage. Licenses and Fees are divided by WP to come up with a percentage.
General expense is divided by earned premium to come up with a percentage.
Projected Premium if given a projected loss ratio and projected pure premium
Pure Premium/Loss Ratio = Projected Premium
If using premium-based expense projection, it’s ok (and probably required) to assume that the fixed expense trend and premium trend will be the same so if you have a projected premium that you are using for fixed expenses, no further trend adjustment is necessary
Fixed expense provision = (calculated percentage)x(Projected Premium)
Shortcomings of exposure based expense projection
• It can result in unfair allocations of countrywide fixed expenses by state, since it doesn’t recognize that expense levels may vary by state
• The existence of economies of scale in a changing book of business will lead to increasing or decreasing future average expenses per exposure.
What to do when you’re told to make an adjustment to a workers compensation indication and you are given: Expenses and profit, Current Deviation (Whatever that means), and expected loss cost difference
The answer will be: (pre-existing indication) x (1/(1-expense and profit)) x (1/current deviation) x (1+expected loss cost difference)
To achieve the primary purposes, briefly describe basic principles that should be present in any sound risk classification system
• The system should reflect expected cost differences.
• The system should distinguish among risks on the basis of relevant cost-related factors.
• The system should be applied objectively.
• The system should be practical and cost-effective.
• The system should be acceptable to the public.
Briefly describe two challenges in territorial ratemaking
i. Territory tends to be highly correlated with other rating variables.
This can distort univariate pricing methods.
ii. Territories are often set to be such small areas (e.g., zip codes) that the data in each territory may have very limited credibility.
Identify the problem with underinsurance from the insurer’s perspective. (why coinsurance requirements are necessary)
The pure premium rate decreases as the policy face increases. If policyholders are underinsured, this is a problem from the insurer’s perspective because if rates are calculated assuming all properties are insured to value, the premium charged will not be adequate to
cover expected losses arising from those policies not insured to value.
An insurance company increases the insurance to value of its book of business. Briefly describe
the impact on each of the following:
• Premium
• Losses
• Expenses
• The direct impact to premium would be an increase in premium due to larger coverage amounts.
However, an indirect impact might be a decrease in premium due to additional cancellations.
• The direct impact to losses would be an increase in the size of the largest claims due to the larger coverage amounts.
However, an indirect impact might be a decrease in losses due to either additional cancellations or new loss control measures implemented by homeowners
as a result of inspections.
• Assuming the increase to ITV is done through a re-inspection program, the cost of the program would likely increase expenses.
However, the increase in expenses relative to the increase in premium is unclear.
Calculating AER for experience mod
- Calculate expected basic limits loss and alae = expected L&ALAE ratio x (Premises/Operations Premium)
- for each experience year, start with result from part 1. and detrend and multiply by eer and % unreported to make expected development
- expected basic limits loss = the sum of (expected basic limits loss x detrend factor) for all experience years
- add the result from 2. to (reported loss and alae (limited by basic limits and MSL)) to make experience ultimate
- AER = experience ultimate/(expected basic limits loss)
Defend the assertion that experience rating supports the principle that a rate should not be unfairly discriminatory
Experience rating recognizes that each risk has a different loss potential, so by modifying the rate appropriately, the expected profit potential for each risk can be made equal. This ensures that equity is achieved and rates are not unfairly discriminatory. Otherwise, risks with lower loss potential within a class would subsidize other higher loss potential risks.
3 factors that can affect claim settlement patterns
• Changes in settlement procedures, such as change in case outstanding strength or claims closure rate. These cause changes in development patterns.
One option is to use Berquist/Sherman adjustments.
• Jury Awards / Legislation / Regulation - these can change type of loss, size of loss, and/or reporting patterns. May need to substitute report year data for accident year because loss may more closely correlate with report date.
• Large Claims - individual large claims can distort reporting and/or payment patterns. One
option is exclude these from the experience and evaluate separately.
how mix of business can affect reserve analysis
• Changes in portfolio volumes - if there is a high growth rate, it can cause distortions in
development factors due to significant shifts in the average accident date in the exposure period. May substitute accident quarter for accident year data.
• Change in policy conditions, such as deductibles, policy limits - this can change the size of
loss distribution, changing the development. May substitute policy year data for accident year data.
• Change in type of business written - this can include change in classes or territories. The different business may have different development patterns or loss ratios.
One option would be to split the data into more homogeneous groups.
Fully explain the value in using frequency-severity techniques
Being able to explicitly reflect inflation in the projection instead of it being included in the selection of development factors is an advantage of the method.
Other advantages are the potential to gain greater insight into the claims process, such as claims reporting, settlement, and avg cost of claims. This helps us to continue to ask the right questions and allows us to find the best estimate of ultimate claims.
Also, freq-sev can be used with paid data only so it is independent of case outstanding changes.
mango-allen refinement for ulae
Similar to classical ulae technique but uses expected paid losses instead of actual. It is useful when insurers have limited or volatile calendar year paid claims.
However, for larger companies with more stable actual paid claims, the extra effort to estimate the expected paid claims may not be justified.
classical ulae development technique
unpaid ulae = W x [Pure IBNR + 50% (Case + IBNER)]
Where W is the selected (Paid ULAE)/(Paid Claims) ratio
IBNER = Total IBNR - Pure IBNR
State the 3 necessary criteria for credibility.
- 0 ≤ Z ≤ 1
- Z should increase as the number of risks increase. dZ/dn≥0
- Z should increase at a non-increasing rate. d/dn(Z/n)<0
remember at the end of the first year losses are 12 months developed
jsyk
fully describe why adverse selection occurs
Adverse selection occurs when an insurer doesn’t use a risk characteristic that is being used by other insurers. Since other insurers will attract the lower risk insureds based on this risk characteristic, the insurer not using the risk characteristic will be left with a higher than
proportional share of the higher risks, for which it does not accurately price or underwrite. As
such, the insurer will have a higher loss ratio.
Excess ratio
Percent of expected losses above the deductible
when does the maximum coinsurance penalty occur
when loss = face value
What loss aggregation method is the best in terms of responsiveness
Calendar year performs the best in terms of responsiveness since there is no loss development.
Briefly define policy year losses
Losses are summarized by the years the policies containing those losses were written
Which loss aggregation method performs the best with respect to matching premiums and losses?
Policy year provides the best match between premiums and losses since the losses come from the same policies from which premium is earned
If given a cumulative paid loss triangle and told to calculate the 2006 CY paid losses.
Take the sum of the 2006 diagonal minus the sum of the 2005 diagonal
Trending incremental paid severity triangle
Trending is done wierdly, each number in the row will have the same trend factor. (normally trend factors are the same on a diagonal basis)
briefly explain practicality with respect to exposure bases
the exposure base should be objective, and easy & inexpensive to obtain and verify
Calculating CY incurred losses
CY incurred loss is all payments made throughout the year + (case reserve at end - case reserve at beginning of year)
If date of loss is after beginning of CY then it CY beginning case reserve is 0.
Disadvantage of using PY losses for ratemaking
the data is the least mature compared to calendar year and accident year loss data
Trend on basic limits losses
(1) apply the selected trend to the ground up losses of each claim
(2) then determine what the total payment on each claim would be under the basic limits.
(3) The basic loss trend is = (sum of all trended basic limits losses from (2)/sum of all untrended basic limits losses)-1
Trend on excess losses
(1) Determine total excess losses (losses above limit - limit)
(2) apply selected trend to ground up losses then determine what total excess losses would be after trending.
(3) Excess loss trend is (2)/(1) - 1
What is a situation in which excess limit trend would be lower than the basic limit trend?
If loss trends are negative, the basic limits trend will be closer to 0 than the more negative excess loss trend
Direct effects should be expressed as percentages
.
What is the retroactive date of a claims-made policy
The earliest date at which a loss can occur and still be covered by a claims made policy
Extended reporting period with relation to claims made policies
An extended reporting period extends the time for which claims that occur during a claims made policy can be reported after the expiration
Identify an advantage and disadvantage of using the trended present rate as the complement of credibility.
An advantage is that it is unbiased. A disadvantage is that it may not be accurate if rate indications have a high process variance.
Formula for indicated territorial relativity
(Credibility weighted Loss Ratio Relativity with complement of credibility)*(Current relativity) then rebase
Complement of credibility is usually 1.0
but if pure premium method: cred weight pp rel with normalized current rel then rebase
Formula for LER
LER(D) = (Sum of all losses capped at D)/(Sum of all losses uncapped)
can also be LER = LAS(D)/LAS(L)
can also be : (Sum of differences in Net Reported Losses across all available coverage levels)/(Sum of Net reported losses of the lower deductible across all available coverage levels)
Indicated deductible relativity = 1-LER(D) = excess ratio
Calculating proposed base rate when given proposed relativies, current relativites and desired overall change
Calculate the the Change factors for all classes = (proposed relativity)/(current relativity).
Then the proposed base rate for class A will be = (Class A current base rate) x(Change factor)x(1+desired rate change)/(Variable premium weighted average change factor)
Two issues that arise when using empirical data to construct increased limit factor tables
• Data often isn’t captured for what claims would have cost in the absence of actual policy limits, so the data is censored.
• Data may need to be developed to ultimate and trended, as higher limits often experience higher development and trends.
How does ITV affect homeowners rate level adequacy?
If the average ITV of the book of business is less than assumed in the insurer’s rates, then the rates will be too low (in the absence of a coinsurance clause or rates varying by ITV).
If the actual average ITV is greater than what is assumed in the rates, then the rates will be too high.
Over time, an insurer can adjust rates so that they are correct overall for the actual level of ITV on the book (assuming it is stable).
Identify and briefly explain two prospective individual risk rating systems.
• Experience Rating - A credit or debit will be assigned to a risk based on the actual loss history of the risk. Larger risks will have more credibility given to their loss experience than smaller risks.
• Schedule Rating - Underwriters assign judgmental credits or debits based on the risk characteristics of particular insured. There should be no overlap in characteristics already implicitly considered in experience rating
Contrast the asset share pricing model to traditional techniques for pricing rate relativities
The asset share pricing model introduces multiple periods, persistency, and different assumptions for new and renewal business.
Weighted average loss development factor
Sum of all next age losses over the sum of their respective this age losses
A benefit of frequency severity disposal rate technique
It uses paid data so it isn’t affected by changes in case reserve adequacy
In reserve analysis, when is report year data preferable to accident year data
If there has been a change in claims department practices such as case reserving guidelines
Formula for Expected Loss emergence based on selected ibnr
Expected loss emergence = selected IBNR x (next age % reported - this age % reported)/(1-this age % reported)
Dollar based ulae approach and count based ulae approach
Dollar based ulae varies by loss amount in dollars. Count based varies by claim count
When should an actuary use basic limits losses for determining an overall rate indication?
Its one way to limit the impact of large individual shock losses on the rate indication.
Applying LAE to Limited Average Severity (also ILF)
LAS= (Las calculated normally)x(frequency)x(1+ULAE Provision)
An advantage of using the ratio method for salvage and subrogation recoverables.
The development factors for the ratio approach tend to be less leveraged than the development factors based on received S&S dollars. Same goes for ALAE ratio.
Round development triangles to dollars
makes things easier
Kittel’s refinements to ULAE reserves
Same general formula as traditional/classic approach: Wx[pure ibnr + .5x(case + ibner)]
Only here the denominator of W is the average of (paid loss & ALAE) and (reported Loss & ALAE). Take the average of the W’s of each experience year for this equation.
Conger’s Expected Claims Approach to ULAE Reserving
Unpaid ULAE = (W x L) - M. (M is paid ULAE)
This approach is flawed for 2 reasons. From a practical perspective, it is difficult to quantify ULAE
on an accident year basis as would be needed in M above to correspond with the accident years in L.
Additionally, this method is not responsive to changes in the ULAE to claims ratio.
Conger’s Bornheutter Ferguson Approach to ULAE Reserving
Unpaid ULAE = W x (L - B)
Where B = Claims Basis used to calculate W.
If 60% of work is expended when claim is reported and 40% is spread over the life of the claim then B = .6xUltimate + .4xPaid.
This is the preferred approach by Conger, and is what is used in the classical and Kittel approaches as well.
Conger’s Development Approach to ULAE Reserving formula and problems
Unpaid ULAE = M x (L/B - 1)
This approach is flawed for 2 reasons. From a practical perspective, it is difficult to quantify ULAE on an accident year basis as would be needed in M above to correspond with the accident years in L. Additionally, this method can be overly responsive to random fluctuations in ULAE emergence.
Issues with other ULAE reserving approaches that led Conger to develop the generalized approach
- Estimates from the traditional approach are inaccurate if the book is changing in size
- The traditional and kittel assumption that 50% of ULAE is spent on opening a claim and 50% is spent on closing may not be a good assumption
4 adjustments made to historical losses in projecting losses for a future policy period.
- Trend
- Development
- Shock losses
- Benefit levels
How does claims-made coverage reduce pricing risk?
Claims made coverage is less impacted by trends, so pricing for these policies is less sensitive to uncertain trend amounts
What is the impact of changing exposure base from number of employees to number of hours worked :
-> Assumption : Proportional to expected loss
• Hours worked is more directly proportional to expected loss than number of employees, so
it would be appropriate to make the change for this reason.
What is the impact of changing exposure base from number of employees to number of hours worked
-> Assumption : Practical
• Hours worked may be more difficult to obtain and verify than number of employees
depending on the recordkeeping of individual companies. For this reason, number of
What is the impact of changing exposure base from number of employees to number of hours worked
-> Assumption : Considerate of historical precedence
• Changing the exposure base would be costly from an IT standpoint and a customer
premium dislocation standpoint, so it would not be appropriate.
What is the impact of changing exposure base from number of employees to number of hours worked
-> Frequency
Since the denominator of frequency (earned exposures) will change, frequency will change.
Since each employee works many hours, hours worked will be larger than number of
employees, so frequency would decline.
What is the impact of changing exposure base from number of employees to number of hours worked :
-> Severity
Since severity is losses per claim count, neither are changing, so there is no impact to severity.
What is the impact of changing exposure base from number of employees to number of hours worked :
->Loss ratio
The impact to loss ratio depends on how the rating algorithm is changed. The numerator of the loss ratio (losses) will remain the same, but the premium may be impacted by the change in exposure, since premiums are calculated on a per-exposure basis and the exposure definition is changing.
5 Data mining techniques
- Factor analysis
- Cluster Analysis
- CART (Classification/Regression tress)
- MARS (Multivariate Adaptive Regression Spline)
- Neural networks
Describe the 3 Adjustments for Shock Losses
- Cap losses at basic limits ( separately derivate rates for excess losss and below low loss)
- Cap losses and apply excess loss loading
Same as previous method but losses are capped at a different amount and apply a loading to cover expected losses above cap level. - Remove ground-up losses and apply shock loss loading (remove -> loading for shock loss added -> back in
What are the two reasons why increased limits loss trends are greater than basic limits loss
trends?
- For losses above the basic limits , inflation will not have impact, but they will impact the excess layer. The trend is entirely in the excess layer
- Losses just under the basic limit are pushed into the excess layer by the trend(inflation) , creating new losses for the excess layer
Two potential distortions when using premium based projection for expense ratios.
Premium trends and rate changes can cause historical expense ratios to be different from the future expense ratios.
Adjusted Pure Premium approach to indicated relativities
Multiply Earned exposures by the weighted average relativity of other factors within the class. Then Calculate Pure Premium. Indicated Relativity will just be adjusted pure premium relativity.
Why is the adjusted pure premium approach to indicated relativities preferable to the pure premium method?
Adjusted takes away the assumption of no correlation between exposures for different rating variables.
Formula : NCCI Experience Mod
Mod = [ZpAp+(1-Zp)Ep+ZeAe+(1-Ze)Ee]/[E]
Where Zp = E/(E+B) and Ze = wxZp
p means primary an e means excess
Ep=(D-factor)x(payroll/100)xExpected Loss Rate
Ee=(1-D-factor)x(payroll/100)xExpected Loss Rate
If overfitting is at all present, then the model is not appropriate.
Even if its only overfit on extreme values and the rest of it seems perfect
Case outstanding development technique is generally more suitable for report year analysis
Why ?
It requires case reserves to provide info about future development, this is more likely to be true when all claims have been reported in the first maturity of the triangle.
Four broad categories of operational changes within an insurance company that could affect an unpaid claims estimate
New Computer Systems, Accounting Changes, Changes in claim handling practices, Changes in Underwriting Guidelines
Disadvantage of using ALAE-to-reported claims ratio method
For some lines of business there may be claims with no claim payment but substantial ALAE.
Two benefits of organizing data for reserving on an accident year basis
More industry benchmarks are available on an AY basis for comparison. Also, it is useful when internal or external events that impact losses are correlated to accident dates.
Considerations for deciding whether to combine lines of business for estimating unpaid claims.
Difference in Case Reserve Adequacy, Difference in Claim settlement rates, Difference in severities, Credibility.
If Credibility is too low for one line then combining them for analysis may be beneficial.
The Three key assumptions underlying the frequency-severity technique
i. Consistent definition of claim counts throughout the experience period.
ii. The mix of the types of claims is relatively homogeneous
iii. Claim Counts and severity will continue to develop in future periods as they have in past periods
3 Criterias for determining if a rating variable should be used
- Is it a differentiator of loss potential?
- is it easy to obtain/verify?
- Does it have a clear definition?
If there is a change in average accident date should you use accident year data?
No use accident quarter data
BF does NOT use on-level premium!
Cape Cod does!
Pay attention to this !
What does negative IBNR imply?
Recoveries such as Salvage and Subro are anticipated
Discuss two reasons it would be acceptable to maintain an imbalance in the fundamental insurance equation at the individual or segment level.
- A regulator might place limits on rate changes or rate differentials across segments.
- If the insurer was using an asset share pricing approach, in which the insurer would look at a longer term view of profitability.
Is it appropriate to perform classification ratemaking analysis using premiums adjusted with aggregate on level factors.
If all past rate changes impacted all classes equally, then it would be reasonable to use aggregate on-level factors. Otherwise no.
Six months after the policy expires, the initial policy premium on every policy increases by 8% due to the final audit
This means there is an extra 8% of premium paid six months after the policy expires
Turning written exposures into earned exposures when there isnt information on when they are written.
Assume half written on 4/1 and the other half written on 10/1 and calculate earned under that assumption.
Data mining techniques
Factor Analysis
MARS
CART
Cluster Analysis
Neural Networks
Data Mining Technique: Cluster Analysis
Combining similar risks into groups, resulting in fewer variables in a GLM.
Data mining Technique: CART
These build a set of if-then rules to identify the most important variables in a GLM. Can detect variable interactions that can be incorporated in a GLM.
Data mining Technique: MARS
Help turn continuous variables into categorical variables by selecting appropriate breakpoints and using piecewise linear approximation. Can detect variable interactions that can be incorporated in a GLM.
Data mining Technique: Neural Network
Helps identify previously unknown interactions between variables that can be incorporated into a GLM.
Key assumption of count based ulae techniques
The same kind of transaction costs the same ULAE regardless of size
Issues with dollar based ulae approaches
- ULAE is not directly proportional to claims
- Using ULAE-to-claims ratios results in volatile ULAE when claims are volatile
Unpaid Claims to Internal Management
Internal Management: The estimates are used to make business decisions in pricing and underwriting, as well as strategic and financial decisions. Inaccurately high estimates could lead to decisions such as raising rates or tightening underwriting guidelines.
Unpaid Claims to Investors
Investors: Changes whether or not the company looks like a bad investment.
Unpaid Claims to Regulators
Regulators: The estimates are used to monitor the solvency of the insurer. inaccurately high estimates resulting in a low profit might cause a regulator to restrict the insurer’s ability to write new business.
Second advantage of the S&S ratio approach
The ratio approach produces ratios of ultimate S&S to ultimate claims, which can be used as a diagnostic. If a ratio for a particular year seems unreasonable, a more reasonable S&S ratio can be selected for that year.
Quota Share Treaty
A Quota Share treaty means that an insurer cedes a constant percent of all claims to the reinsurer. As such, the net claims will be a constant percent of gross claims.
Excess of Loss Treaty
A per-risk or per-occurrence Excess of Loss (XOL) treaty means that the insurer will cede all amounts above a certain retention and up to a certain limit on individual claims.
Stop Loss Treaty
A Stop Loss treaty, also known as an Aggregate Excess of Loss treaty, means that the insurer will cede all amounts above a certain retention on the aggregate loss amounts for the insurer’s book
Tail factor for quota share treaty
For Quota Share treaties, the tail factors for gross, net, and ceded triangles will be the same since the net and ceded triangles are just constant multiples of the gross triangle.
Tail factor for XOL and Stop Loss treaty
The tail factor for the ceded triangle will typically be larger than for the gross triangle since once the retention is hit, all development occurs in the ceded layer. The tail factor for the net triangle will typically be smaller than for the gross triangle since the net losses may be capped by the reinsurance protection.
3 approaches to estimating ALAE
- Combining ALAE with Claims and estimate them together
- Develop an ALAE triangle separately
- Ratio approach that develops ALAE to Paid Claims
The 4 principles of P&C ratemaking:
- A rate is an estimate of the expected value of future costs.
- A rate provides for all costs associated with the transfer of risk.
- A rate provides for the costs associated with an individual risk transfer
- A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is an actuarially sound estimate of the expected value of all future costs associated with an individual risk transfer.
Adjustment to losses for changes in benefit levels
Just use parallelogram method
Skimming the cream
Identifying a lower cost group of insureds that has not been identified by the competition and recognizing that difference in underwriting or marketing instead of rating
3 Primary Purposes of risk classification
- Protect the insurance systems financial soundness
- Enhance Fairness
- Permit economic incentives to operate and thus encourage widespread availability of coverage.
Why do Small workers comp insureds tend to have worse loss experience than larger insureds
- Small companies usually have less sophisticated safety programs
- Small companies usually dont have return-to-work programs for injured workers
- Not as impacted or do not qualify for experience rating, so they have less incentive to mitigate risks
6 desirable qualities for complement of credibility
- accurate (close to the target)
- Unbiased (On target on average)
- Statistically independent from the base statistic
- Available (other wise not practical)
- Easy to compute
- Logical relationship to base statistic
Actions that can be taken to respond to regulatory restrictions
- Take legal action
- Revise UW guidelines to limit bus at inadequate rates
- Revise marketing to limit bus at inadequate rates
- Use proxy variable when a variable is prohibited
ISO questions: driving record
There will be no mid-term charge for changes in the driving record sub-classification.
Even the most recent experience year has a first step trend factor if latest WP is different from earned
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