Marshall

Question 1

Claims portfolio

Answer 1

= aggregate portfolio for which risk margins must be estimated

Question 2

valuation classes

Answer 2

portfolios are considered individually as part of risk margin analysis

Question 3

claim group

Answer 3

group of claims with common risk characteristics

Question 4

sources of uncertainty: 2 sources

Answer 4

1. systematic risk
2. independent risk

Question 5

systematic risk and 2 types

Answer 5

Systemic risk = risks that are common across valuation classes or claims groups

• internal
• external

Question 6

independent risk and 2 types

Answer 6

Independent risk = risk that occur due to randomness inherent in insurance process

• parameter risk = extent to which randomness associated with insurance process affects ability to select appropriate parameters
• process risk = pure effect of randomness associated with insurance process

Question 7

internal systematic risk definition and 3 sources

Answer 7

internal = risks internal to liability valuation/modeling process

1. Specification error
2. parameter selection error
3. data error

Question 8

Specification error

Answer 8

Specification error = arises b/c model cannot perfectly model insurance process

Umbrella claims are more variable due to longer tail and high attachment point

Potential risk indicator = number of models run

Question 9

Parameter selection error

Answer 9

Parameter selection error = arises b/c model cannot adequately measure all predictors of future claim costs or trends in these predictors

Severity trend have larger impacts on excess layers

Risk indicator = predictors stable over time?

Question 10

Data error

Answer 10

Data error = arises due to lack of credible data and inadequate knowledge of portfolio being analyzed

Risk indicator = data timely, reliable, and consistent?

Question 11

external systematic risk definition and 7 sources

Answer 11

external = risks external to valuation/modeling process

1. economic and social
2. legislative political, & claims inflation
3. claims management process change
4. expense
5. event
6. latent
7. recovery

Question 12

Economic and social risk

Answer 12

uncertainty associated with inflation, social trends, etc

Question 13

Legislative, political, & claims inflation risk

Answer 13

uncertainty associated with changes in political landscape, shifts/trends in level of settlement etc

WC benefit levels

Question 14

Claims management process change risk

Answer 14

uncertainty associated with changes in claim reporting, payment, estimation, etc

Question 15

expense risk

Answer 15

uncertainty associated with cost of managing runoff or maintaining unexpired risk until date of loss

Question 16

event risk

Answer 16

uncertainty associated with claim costs arising from events, natural or man made

Property for CATs

Question 17

Latent claims risk

Answer 17

uncertainty associated with claims that arise from sources that are not currently covered (asbestos)

WC for asbestos

Question 18

recovery risk

Answer 18

uncertainty associated with recoveries either reinsurance or non-reins

-risks will typically be included in central estimate valuation so best to analyze in conjunction with central estimate valuation

Question 19

correlation effects

Answer 19

Independent risk: assumed to be uncorrelated with any other source of uncertainty either within valuation class or btw classes

Internal: assumed to be uncorr with ind risk and each source of external, but internal tends to be correlated btw VCsand between OCLs and PLs

External: assume each risk category is uncorrelated with independent and internal, but correlations may exist between risks that belong to similar risk categories or may be correlations for common risk course across multiple classes like event risk for different LOBs

Question 20

why is internal systemic risks tend to be correlated?

Answer 20

between VCs: same actuary effect and template models/similar models used across valuation classes

between OCLs and PLs: linkage between PL and OCL methodologies

Question 21

risk margin: normal distribution

Answer 21

risk margin = Z*CoV

normal produces higher risk margin at lower probability of reserve adequacy

Question 22

risk margin: lognormal distribution

Answer 22

risk margin = exp(u+Z*σ)/sum(weights)-1

CoVs inform calculation of u and σ

lognormal distribution produces higher risk margin at higher probability of reserve adequacy

Question 23

risk margins can be converted into dollars

Answer 23

by multiplying them by central estimates

Question 24

if no correlation, CoV

Answer 24

CoV = sqrt(Σ(wi*CoVi)²)/Σwi

used by independent risk

Question 25

if correlation, CoV

Answer 25

need to incorporate 2*row*w1*w2*CoV1*CoV2 in formula for each pair that has correlation

*internal systemic risk uses this

Question 26

CoV formula for external risks

Answer 26

CoV^2=ΣCoV(i)^2

assuming independence for external sources of risk

Question 27

CoVs should be subjected to

Answer 27

internal checks

Question 28

For each source of uncertainty, CoVs should be compared

Answer 28

• btw VCs for OCLs, PLs, and total insurance liability
• comparison should be made between OCLs and PLs within classes

Question 29

For independent risk, internal benchmarking for 2 main dimensions

Answer 29

• portfolio size: larger portfolio, lower volatility arising from random effects
• length of claim run-off: longer run-off, more time there is for random effects to have an impact

Question 30

2 dimensions for internal benchmarking for independent risks has implications for CoV selections

Answer 30

• OCL CoVs for short-tailed < similar sized long-tailed
• OCL CoVs for short-tailed < smaller long-tailed
• PL CoVs for long-tailed > OCL for same portfolio due to law of large numbers

PLs should be smaller resulting in more volatility

Difference should be larger for small portfolios with higher independent risk components

-PL CoVs for short-tailed < OCL for same portfolio due to law of large numbers

PLs will be larger since most of OCLs will have already closed -> less volatility for PLs

Question 31

for internal systemic risk using internal benchmarking, CoVs patterns/rules

Answer 31

• classes with homogeneous claim groups should have similar CoVs
• long-tailed portfolios should have higher than short-tailed since long-tailed tend to be more complicated

Question 32

for external systemic risk using internal benchmarking, CoVs patterns

Answer 32

• long-tailed should have higher than short-tailed in most cases
• exceptions = event risk and liability risk for home classes

Question 33

claims portfolio should be split into valuation classes

Answer 33

• choice of classes must ensure that classes grouped together are homogenous and in line with central estimate valuation
• to reduce risk (of selection in parameters, etc.), they must have similar characteristics (ex. development pattern) and must be sufficiently large datasets to ensure reasonable credibility
• approach should balance practical benefits gained from higher level allocation with insight gained from more granular allocation
• once divided into VC, must determine whether or not specific classes should be divided further into claims group

Question 34

Questions to ask management for segmentation of portfolio

Answer 34

-CAT event in any geo location?

CATs have diff development patterns than normal loss -> model CAT losses separately

-are coverages the same in all locations?

Diff coverages have diff development patterns

-are there differences in regulation for locations?

Development patterns may differ due to diff in regulation

Question 35

balance scorecard: reasonableness/general rules

Answer 35

• minimum CoV for best practice shouldn’t be much below 5% because even a perfect model won’t be able to completely represent the true underlying process
• comparing LOBs: the LOB with a longer tail should have a higher CoV at each score due to difficulty in modeling long tailed LOBs
• scale should not be linear because marginal improvements will have diminishing returns

Question 36

calculate internal systemic risk CoV when you have balance scorecard

Answer 36

score(LOBi)=Σ(scorei*wi)/Σwi

look up scores on the CoV scale

Question 37

important to do sensitivity testing for risk margin calculation

Answer 37

risk margin has many underlying assumptions

need to understand which assumptions impact final risk margin the most

Question 38

single model with limited data that scored poorly against compared to best practice could have internal systemic risk CoV

Answer 38

> 20%

Question 39

internal systemic risk: quantitative modeling techniques

Answer 39

quantitative modeling could be used to inform the approach but balances scorecard process to assess risk indicators should be used

Question 40

external systemic risk: quantitative modeling techniques

Answer 40

quantitative modeling can analyze past episodes of external systemic risk, but cannot adequately capture potential future external systemic risks to extent they’re different than the past

Question 41

independent risk: quantitative modeling techniques

Answer 41

stochastic modeling techniques such as Mack method, Bootstrapping, or Bayesian techniques are appropriate to assess independent risk

Question 42

why when assessing risk margins shouldn’t directly use quantitative methods to select correlations between valuations classes for sources of risk

Answer 42

quantitative methods to estimate correlations are technically complex and require lots of data

correlations would be heavily influences by past events and may not be appropriate for future

would be difficule or impossible to break out correlations to different risk sources

therefore, should use judgement to select correlation coefficients to assess risk margins