Brehm ch.3 Flashcards
1
Q
what does implementing an IRM require beyond data collection and model running?
(Brehm ch.3)
A
- planning
- organizational change
- leadership
- communication
2
Q
what are six organizational details of implementing IRMs that need to be addressed early on?
(Brehm ch.3)
A
- organization chart
- functions represented
- resource commitment
- critical roles and responsibilities
- purpose
- scope
3
Q
what org chart considerations should be assessed when implementing IRMs?
(Brehm ch.3)
A
- modeling team reporting line
- solid line vs. dotted line reporting
4
Q
what considerations about functions represented should be assessed when implementing IRMs?
(Brehm ch.3)
A
- reserving
- pricing
- finance
- planning
- underwriting
- risk
5
Q
what resource commitment considerations should be assessed when implementing IRMs?
(Brehm ch.3)
A
- mix of skill set (UW, actuarial, communication, etc.)
- full time vs. part time
6
Q
what critical roles and responsibilities should be assessed when implementing IRMs?
(Brehm ch.3)
A
- control of input parameters
- control of output data
- analyses and uses of output
7
Q
what purpose consideration should be assessed when implementing IRMs?
(Brehm ch.3)
A
is the goal of the model to quantify variation around the plan?
8
Q
what scope considerations should be assessed when implementing IRMs?
(Brehm ch.3)
A
- prospective UW year only or including reserves, assets, operational risks?
- low detail (whole company) or high detail (on specific segment)?
9
Q
what do Brehm et. al recommend re: reporting relationship when implementing IRMs?
(Brehm ch.3)
A
reporting line for IRM team is less important than ensuring they report to a leader who is fair
10
Q
what do Brehm et. al recommend re: resource commitment when implementing IRMs?
(Brehm ch.3)
A
best to transfer internal employees or hire external employees for full-time positions
11
Q
what do Brehm et. al recommend re: inputs and outputs when implementing IRMs?
(Brehm ch.3)
A
controlled in a manner similar to that used for general ledger or reserving systems
12
Q
what do Brehm et. al recommend re: initial scope when implementing IRMs?
(Brehm ch.3)
A
- prospective UW period
- variation around plan
13
Q
what four parameter development details need to be addressed when implementing IRMs?
(Brehm ch.3)
A
- modeling software
- developing input parameters
- correlations
- validation and testing
14
Q
what are modeling software considerations when implementing IRMs?
(Brehm ch.3)
A
- capabilities
- scalability
- learning curve
- integration with other systems
15
Q
what are three considerations when developing input parameters to implement IRMs?
(Brehm ch.3)
A
- process heavily data driven
- requires expert opinion (especially with low data quality)
- many functional areas should be involved
16
Q
what needs to be addressed about correlations when implementing IRMs?
(Brehm ch.3)
A
-LOB reps cannot set cross-line parameters -> corporate-level ownership is required
17
Q
what are validation and testing considerations when implementing an IRM?
(Brehm ch.3)
A
- no existing IRM with which to compare
- multi-metric testing
18
Q
what do the authors recommend for modeling software re: parameter development for IRMs?
(Brehm ch.3)
A
- compare existing vendor software with user-built options
- ensure final software choice aligns with capabilities of the IRM team
19
Q
what do the authors recommend when developing input parameters for IRMs?
(Brehm ch.3)
A
- include product expertise from UW, claims, planning, and actuarial
- develop systematic way to capture expert opinion
20
Q
what do the authors recommend when development correlation parameter details for IRMs?
(Brehm ch.3)
A
- have IRM team recommend correlation assumptions
- ultimately own those at the corporate level
21
Q
what do the authors recommend for validating and testing IRMs?
(Brehm ch.3)
A
- validate and test over extended period
- provide basic education to interested parties on probabilities and statistics
22
Q
what four IRM implementation details need to be addressed?
Brehm ch.3
A
- priority setting
- interest and impact
- pilot test
- education process
23
Q
what priority setting details need to be addressed for IRM implementation?
(Brehm ch.3)
A
- importance of priority (company may not immediately make necessary improvements to support implementation)
- approach and style (ask vs. mandate)
- priority and timeline must be driven from the top
24
Q
what interest and impact details need to be addressed for IRM implementation?
(Brehm ch.3)
A
-implement communication and education plans across the enterprise
25
what pilot testing details need to be addressed for IRM implementation?
(Brehm ch.3)
- assign multidisciplinary team (actuarial, UW, finance, etc.) to provide real data and real analysis on the company as a whole or one one specific segment
- piloting means model indications receive NO WEIGHT
26
what education process details need to be addressed for IRM implementation?
(Brehm ch.3)
- run in education process in parallel with pilot test
| - bring leadership to same point of understanding regarding probability and statistics
27
what do the authors recommend for priority setting for IRM implementation details?
(Brehm ch.3)
have top management set the priority for implementation
28
what do the authors recommend for interest and impact details for IRM implementation?
(Brehm ch.3)
plan for regular communication to broad audiences
29
what do the authors recommend for pilot testing for IRM implementation?
(Brehm ch.3)
prepare the company for the magnitude of change resulting from using an IRM
30
what do the authors recommend for education process for IRM implementaiton?
(Brehm ch.3)
-target training to bring leadership to a similar BASE level of understanding
31
what three IRM integration and maintenance details need to be addressed?
(Brehm ch.3)
- cycle
- updating
- controls
32
what details re: IRM cycle need to be addressed?
| Brehm ch.3
- integrate model runs into major corporate calendar (planning, reinsurance purchasing, capacity allocation)
- ensure that IRM output supports major company decisions
33
what details re: updating IRMs need to be addressed?
| Brehm ch.3
determine frequency and magnitude of updates
34
what control details for IRMs need to be addressed?
| Brehm ch.3
- ensure there is centralized storage and control of input sets and output sets (date sampling vital)
- ensure there is an endorsed set of analytical templates used to manipulate IRM outputs for various purposes (such as decision making and reporting)
35
what do the authors recommend for IRM integration and maintenance cycle?
(Brehm ch.3)
integrate into planning calendar at a minimum
36
what do the authors recommend for IRM updating?
| Brehm ch.3
- perform major input review no more frequently than twice a year
- minor updates can be handled by modifying the scale of the impacted portfolio segments
37
what do the authors recommend for IRM controls?
| Brehm ch.3
-maintain centralized control of inputs, outputs, and application templates
38
in what three ways does the risk of assuming incorrect distributions or parameters for estimating F and S distributions for each LOB manifest itself?
(Brehm ch.3)
- estimation risk
- projection risk
- model risk
39
what is estimation risk?
| Brehm ch.3
arises from using only a sample of the universe of the possible claims to estimate the parameters of the distribution
40
what is projection risk?
| Brehm ch.3
arises from projecting past trends into the future
41
what is model risk?
| Brehm ch.3
arises from having the wrong models to begin with
42
if severity distributions are identical, but one company has a larger frequency distribution, how would their CV for aggregate losses compare?
(Brehm ch.3)
-much higher for company with smaller frequency mean
43
if severity distributions are identical, but one company has a larger poisson F mean, and losses are multiplied by random factor (1+J), how do the impacts to CV for each company compare?
[1+J is constant for all claims for a year and has a mean of 1]
(Brehm ch.3)
- as CV(1+J) rises, the risk for larger companies rises as well
- much less pronounced for smaller companies since they're already volatile
44
how can projection risk be quantified for a simple trend model (trend line fit to loss cost history)?
(Brehm ch.3)
-prediction intervals can be placed around the projection
45
in the projection period, what is the projection uncertainty a combination of?
(Brehm ch.3)
- uncertainty in each historical point
- uncertainty in fitted trend line
- -> spread in prediction intervals increases in projection period
46
how does claim severity trend tend to differ from general inflation?
(Brehm ch.3)
- claim severity trend is often greater
| - excess trend is often described as social inflation or superimposed inflation
47
what is an approach to modeling severity that considers general inflation?
(Brehm ch.3)
- correct payment data using general inflation indices
- model residual superimposed inflation
* *any subsequent projection is of superimposed inflation ONLY, need separate general inflation projection
48
what is an advantage of projecting superimposed inflation and general inflation separately?
(Brehm ch.3)
- reflects the dependency between claim severity trend and general inflation
- ->inflation uncertainty is incorporated into projection risk
49
what does the simple trend model assume?
| Brehm ch.3
- assumes there is a single underlying trend rate that has been constant throughout the historical period and will remain constant in the future
- only potential error is misestimation of rate
50
what is the general structure of a first order autocorrelated time series (AR-1)?
(Brehm ch.3)
- mean-reverting time series
- true mean unknown and estimated from data
- includes autocorrelation coefficient and annual disturbance distribution
51
how do prediction intervals change over time for the simple model vs. the AR-1 model?
(Brehm ch.3)
- for both models, prediction intervals widen with time due to the uncertainty in the estimated trend rate
- more pronounced to AR-1 & intervals are wider due to additional uncertainty
52
in long-tailed lines of business with a long projection period, which trend model is preferred and why?
(Brehm ch.3)
- prefer AR-1
| - simple trend likely understates projection risk
53
what is a challenge of parameterizing time series?
| Brehm ch.3
if time period of data is too limited to exhibit a range of behaviors, resulting model will be limited too, and will understate projection risk
54
what is the preferred method for estimating parameters of frequency and severity distributions from historical data?
(Brehm ch.3)
maximum likelihood estimation (MLE)
55
what is the likelihood of a distribution for a set of data?
| Brehm ch.3
probability of observing that data from a samle of that size from the (F/S) distribution
56
when might the best-fitting parameters be difficult to determine by MLE?
(Brehm ch.3)
-if likelihood "surface" is very flat near the maximum -> wide range of parameter sets have almost the same likelihood --> set that maximizes likelihood might not be any better than one that has slightly smaller likelihood
57
what is the information matrix?
| Brehm ch.3
-matrix of all second partial derivatives of the negative of the log-likelihood
58
what is the inverse of the information matrix?
| Brehm ch.3
covariance matrix for the parameters of the distribution
59
for large data sets, what are the parameter distributions in the MLE procedure?
(Brehm ch.3)
multivariate normal
60
why does the normality assumption for parameter distributions in the MLE procedure create problems?
(Brehm ch.3)
- SD of parameters can be high enough to produce negative param values with significant probability
- distribution of parameters may be heavy-tailed (bi-variate normal is not heavy-tailed)
- simulation tests on small samples have found that log-normal distributions provide a good fit to the parameter distributions
61
how do we assess estimation risk?
| Brehm ch.3
- use covariance matrix from standard MLE procedure
| - assume params follow a joint logN distribution
62
how do AIC and BIC consider parameters when evaluating models?
(Brehm ch.3)
penalize models that use a large number of params
63
what type of AIC/BIC is desirable, and what does this indicate?
(Brehm ch.3)
- low is desirable
| - indicates model that fits well AND has less complexity
64
what is another statistic similar to AIC/BIC?
| Brehm ch.3
Hannan-Quinn Information Criteria (HQIC)
65
what are five recommendations to overcome the possibility of selecting the wrong distribution?
(Brehm ch.3)
- assign probabilities of being right to all of the better-fitting distributions (based on HQIC or Bayesian analysis)
- use simulation model to select distribution
- select params from joint logN distr. of params
- simulate loss scenario
- start process over again
66
what is parsimony?
| Brehm ch.3
less model complexity
67
what can too much parsimony produce?
| Brehm ch.3
unrealistically stable results
68
why is some model complexity required?
| Brehm ch.3
to ensure that the model is capturing the true uncertainty of the underlying process
69
how does the correlation between auto and property insurance (or any two correlated lines) need to be reflected in IRMs?
(Brehm ch.3)
by incorporating more weight into the right tail of the multivariate distribution describing the SUM of the lines
70
what is a copula?
| Brehm ch.3
a function that combines individual marginal distributions (ex: auto and property lines) into a multivariate distribution
71
what does C(0.3, 0.2) represent?
| Brehm ch.3
- the probability that u < 0.3 and v < 0.2
| - probability that F_X(x) < 0.3 and F_Y(y) < 0.2
72
what kind of correlation in the tails does the Frank copula produce?
(Brehm ch.3)
weak tail correlation
73
how does tail concentration in the Gumbel copula compare to Frank?
(Brehm ch.3)
-more tail concentration
74
what is the general shape of the Gumbel copula?
| Brehm ch.3
asymmetric with more weight in the right tail
75
what does the heavy right tail Copula look?
| Brehm ch.3
-less correlation in left tail and more correlation in right tail
76
when does a HRT copula produce a joint Burr distribution?
| Brehm ch.3
- if X and Y are Burr distributions AND
| - a parameter of both Burr distributions is the same as that of HRT copula
77
what are two advantages of the normal copula?
| Brehm ch.3
- easy simulation method
| - generalizes to multi-dimensions (i.e. greated than two dimensions)
78
how does the normal copula right tail compare to the other copulas?
(Brehm ch.3)
- lighter than Gumbel and HRT copulas
| - heavier than Frank copula
79
order the tails of the Gumbel, Frank, HRT, and normal copulas, from lightest to heaviest
Frank < Normal < Gumbel < HRT
80
what are three ways to fit copulas to data?
| Brehm ch.3
- MLE
- minimize SSE between empirical and fitted copulas
- look at descriptive functions (ex: tail concentration functions) to judge goodness of fit
