Teng & Perkins Flashcards
Describe Premium Asset
Ult prep that insurer expects to collect based on expected ult loss. experience less premium that insurer has already booked
= Retro P - Collected P
3 reasons why retro policies are popular
- They encourage loss control and loss management by returning premium to the insured for good loss experience.
This is great for the insurer as well because it attracts preferred customers. - They offer CF advantage to insureds by allowing them to pay premium as losses are reported or paid.
- Since premium varies directly with the insured’s actual loss experience, it shifts a large portion of the risk to the insured.
This is great for the insurer due to the increasing difficulty in predicting the cost of insurance.
Calculate premium under retro policy
Pn = (BP + (CLnLCF))TM
BP is the Basic Premium
CLn is the capped Loss at nth adjustment
LCF is the loss conversion factor
TM is the tax multiplier
Calculate PDLD ratio at first and subsequent adjustment
PDLD1 = (BP/SP)TM/(ELR%Loss1)+(CL1/L1)LCFTM
PDLDn = (CLn - CLn-1)/(Ln - Ln-1) * LCF * TM
PDLDn = Inc Loss Capping Ratio at n * LCF * TM
Calculate basic premium factor
BP/SP
Calculate the expected loss ratio for the first adjustment
ELR * % Loss Emergence at first adjustment
Calculate the cumulative loss capping ratio for the first and subsequent adjustments
CL1 / L1
CLn/Ln = 1 - Net Ins Charge - LER
Net Ins Charge = Charge at Max - Savings at Min
Briefly describe the relationship between loss capping ratio and development of losses.
The loss capping ratio decreases as the data becomes more mature since an increasing portion of the loss development occurs outside of loss limitations.
At each subsequent retro adjustment, more losses reach their maximum premium and more losses are capped by per accident limit. Thus, the capping ratios decrease for later retro adjustments.
State 1 advantage and 1 disadvantage of the retro PDLD formula approach.
Advantage:
1. Responsive to changes in retro rating parameters that are sold.
If parameters change significantly, should give more weight to retro formula PDLD ratios rather than those from historical data.
2. Empirical PDLD ratios can be volatile. Formula approach ratios are more stable.
Disadvantage:
Must select retro rating parameters.
This may be difficult because parameters will vary between policies sold.
Bias may exist since PDLD formula uses average parameters.
Which types of data are needed for the empirical approach (2)
- Booked premium development
- Reported loss development
Calculate PDLD at first and subsequent adjustment using the empirical formula approach.
PDLD1 = Prem@27m / Loss@18m
PDLD2 = (Prem@39m - Prem@27m) / (Loss@30m - Loss@18m)
PDLDn = Delta Prem / Delta Loss
Briefly explain two causes of upward trend in PDLD ratios
- More liberal retro rating parameters (change in retro parameters being sold), such as a higher max, min or per accident limitation.
- Improvement in loss experience, resulting in a larger portion of loss being within the boundaries of the retro max and per accident limitation.
This drives additional premium per dollar of unlimited loss.
Briefly explain why historical PDLD fluctuate significantly after first retro adjustment.
Premium and loss development on a few policies can drive total incremental development on quarterly data.
Negative PDLD ratios are possible if upward development in high loss layers (resulting in no additional premium) and downward development in layers within loss limitations (resulting in return premium).
If large fluctuation exists, average as many historical points as possible OR use the formula approach.
Briefly describe 2 reasons why formula PDLD and historical PDLD ratios could diverge.
- Worse (or better) than expected loss experience may have caused a larger portion of the loss to be outside (inside) the boundaries of the retro max and per accident limitation than formula approach predicted.
- Average retro parameters may be changing over time.
Describe CPDLD ratios
Cumulative PDLD
Average of the PDLD ratios in all subsequent retro periods (including current adj period), weighted by % Loss Emergence in each period.
It tells an insurer how much premium it can expect to collect for a dollar of loss that has yet to emerge.
3 reasons why CPDLD ratio at first retro adj is normally greater than 1.0
- First retro premium computation includes the basic premium
- Only a small portion of loss is limited at this point
- Application of the loss conversion factor and tax multiplier results in more than a dollar of premium per dollar of loss.
At subsequent adjustments, CPDLD ratio should be less than 1 due to retro max and per accident limitation.
Calculate CPDLD
CPDLDn = sum(PDLDn*%Lossn) / sum(%Lossn)
Calculate the Prem Asset
Expected Future Loss Emergence = Ult Loss - Loss @ Prior Adj
Expected Future Premium = Expected Future Loss * CPDLDn
Ult Prem = Retro P = Expected Future P + Booked Prem @ Prior Adj
Prem Asset = Ult Prem - Current Booked Prem
Describe the graphical representation of the Fitzgibbon method vs the Enhanced PDLD method
Name 3 issues to consider in Prem Asset calculation
- ALAE
Def of loss may include ALAE
Make sure data used in computing PDLD rails is consistent with that used in rating plan. - Mix of business
Changes in mix by state, industry group or geo region may change PDLD ratio.
This can alter average rating parameters sold and the underlying claim freq and severity. - Collectability
If a portion of premium asset is not secured, then a provision should be made to anticipate bad debt.
3 advantages of PDLD method over other methods for estimating premium asset (feldblum review)
- It is modelled directly on retro rating formula, making it easy to explain
- Its focus on premium sensitivity is similar to how loss sensitive contracts are handled under risk-based capital.
- It may be useful when changes to retro rating parameters distorts indications from other methods.
3 reasons why not estimate accrued retro premium Asset using a chain-ladder approach.
- Due to the lag in processing and recording retro premium adjustments, a C-L estimate of premium asset is not available until at least 9 months after the policy expiration, an it can be updated only annually thereafter.
- An initial estimate of the premium asset can be produced soon after policy expired using the known loss information and the relationships between incurred losses and retro premium.
- The premium asset estimate can also be updated each quarter as new loss data becomes available.
Calculate Retro Premium using Fitzgibbon’s Method
Y = A + B*X
Y = Retro P / SP
X = Ult Loss / SP
A = B/SP
B = Premium Responsiveness
2 disadvantages of Fitzgibbon’s Method
- If retro premium-to-date has been less responsive than expected, there is no way to correct because the method estimates ultimate premium based on cumulative loss-to-date.
- Fitzgibbon uses a constant slope, but we would expect the slope to decrease for more mature losses and higher overall loss ratios because of loss limits and maximum premiums.
3 reasons why slope B is not exactly 1 in Fitzgibbon’s Method
- Loss limitations (i.e. retro max and per-accident limit)
- Minimum premiums might excess basic premium
- LCF and TM are applied to incurred losses, which changes the slope.
Briefly describe the Berry’s Method
Modifies Fitzgibbon’s method by gradually discarding the method and giving more weight to the actual experience of the book of business.
State the 2 Teng & Perkins PDLD Assumptions
- Premium responsiveness for future adjustments is independent of premium responsiveness of past adjustments.
- The slope of the line segment (premium responsiveness) is independent of the beginning loss ratio and the beginning retro premium ratio.
These 2 assumptions fix the issues in Fitzgibbon’s method.
Describe the relationship between premium responsiveness and:
a) book age
b) loss ratio
a) Premium responsiveness decreases as the book matures
L’argüer % of losses is excluded by loss limits and max premium
b) Premium responsiveness decreases for higher loss ratios
Policies are more likely to hit max premium
Describe Feldblum enhancement method
Feldblum suggests we subtract the average basic premium charge as a ratio to the std loss ratio (BP/SP / ELR) from the first CPDLD ratio.
CPDLD1* = CPDLD1 - TM*BP/SP / ELR
Discuss why incremental premium can be greater than incremental losses at first adjustment.
First adjustment premium includes basic premium, amount charged even if there are no losses.
Also, fewer losses are capped by first adjustment period, which contributes to PDLD ratio to be greater than 1.
Explain how observed premium development to loss development (PDLD) ratio could become negative.
Assume losses on claims below loss limits decreased, resulting in incremental premium to be negative. If losses on claims above loss limits increased by more than losses on claims below loss cap, then incremental premium would be negative despite the fact that incremental losses were positive.
Assuming all claims are greater than plan minimum, explain how a push to settle small claims faster would impact PDLD ratios.
It will increase capped loss ratios for earlier adjustments (since larger % losses a earlier adjustments will be below cap).
This will cause early PDLD ratios to increase, because each claim will create additional premium.
When more of the small claims are settled earlier, incremental capped loss ratios will decrease for later adjustments, because remaining losses are larger and hit the cap.
This will cause later PDLD ratios to decrease.
1 advantage of using chain-ladder development method on historical earned premium triangles.
Responsive to how premiums have developed historically.
Explain why slopes differ between Fitgibbon’s linear regression method and PDLD method.
PDLD method relates to premium responsiveness to reported losses and recognizes that this responsiveness (slope) decreases over time has more losses are capped, min/max are applied, etc.
Fitzgibbon method relates premium responsiveness to ultimate losses so slope is constant.
Describe the empirical PDLD ratios method
Use booked premium triangles and loss development triangles to select PDLDs.
