Shapland and Leong

Question 1

Two advantages of bootstrapping

Answer 1

1) Allow us to calculate likelihood that claims will exceed certain amount
2) Able to reflect skewness of insurance losses

Question 2

One disadvantage of bootstrapping

Answer 2

More complex and time consuming

Question 3

How using ODP relates GLM to standard CL

Answer 3

Start with latest diagonal and divide backwards to obtain fitted incrementals

Question 4

Three important outcomes from using ODP to relate GLM to standard CL

Answer 4

1) Simple link ratio algorithm
2) LDFs bridge to deterministic framework (more easily explainable)
3) In general, loglink function does not work for negative incrementals

Question 5

Assumptions underlying residual sampling process

Answer 5

Residuals are iid

Question 6

Two uses of degrees of freedom adjustment factor

Answer 6

Distribution of reserve estimates could be multiplied by factor for over-dispersion of residuals in sampling process; Pearson residuals can be multiplied to correct for bias

Question 7

Downfall of degrees of freedom adjustment factor

Answer 7

Does not create standardized residuals

Question 8

Benefit of bootstrapping incurred triangle

Answer 8

Leverages case reserves to better predict ultimate claims

Question 9

One deterministic method for reducing variability in extrapolation of future incremental values

Answer 9

BF method

Question 10

Four advantages to generalizing ODP

Answer 10

1) Fewer parameters
2) Can add parameters for CY trends
3) Can model data shapes other than triangles
4) Can match model parameters to statistical features found in data

Question 11

Two disadvantages to generalizing ODP

Answer 11

GLM must be solved for each iteration; time-consuming

Question 12

Disadvantage to including CY trends in ODP/remedy

Answer 12

GLM no longer has a unique solution/start with a single parameter and add as needed

Question 13

Four options for dealing with negative incremental values in ODP

Answer 13

1) Remove extreme iterations
2) Recalibrate model
3) Limit incrementals to zero
4) Use more than one model

Question 14

Why average of residuals from ODP may differ from zero in practice

Answer 14

Different AYs develop at different rates relative to weighted average

Question 15

Arguments for and against adjusting residuals to average to zero

Answer 15

For: re-sampling adds variability to resampled incremental losses
Against: It is a characteristic of the data set

Question 16

How to adjust residuals of ODP to overall mean of zero

Answer 16

Add single constant to all residuals such that sum of shifted residuals is zero

Question 17

Three approaches to managing missing values in triangle

Answer 17

1. Exclude
2. Estimate using surrounding values
3. If missing value lies on last diagonal, use value in second to last diagonal to construct fitted triangle

Question 18

Three approaches to managing outliers in the loss triangle

Answer 18

1. If on first row, we can delete row
2. Exclude completely
3. Exclude when calculating LDFs but re-sample

Question 19

Difference between homoscedastic and heteroscedastic residuals

Answer 19

Homo - residuals are iid

Hetero - independent but not independently distributed

Question 20

Two options to adjust residuals for heteroscedasticity

Answer 20

Stratified Sampling
Variance parameters (hetero-adjustment factors)

Question 21

Interaction between heteroscedasticity and credibility

Answer 21

Important not to overact to apparent heteroscedasticity in older development years

Question 22

Heteroechtesious data

Answer 22

Incomplete or uneven exposures at interim evaluation dates

Question 23

Two types of heteroecthesious data

Answer 23

Partial first development period (first column has different exposure period than rest of column)
Partial last calendar period data (six month diagonal)

Question 24

Diagnostic tests to assess quality of stochastic model

Answer 24

1. Test assumptions in model
2. Gauge quality of model fit
3. Guide adjustment of model parameters

Question 25

Red flags in an output from bootstrap model

Answer 25

1. Standard errors should increase over time
2. Reserves should be increasing over time
3. CoV should decrease over time
4. Total standard error should be larger than any individual AY

Question 26

Two reasons why CoV may rise in most recent AYs

Answer 26

Increasing parameter uncertainty

Simple overestimation of recent variability

Question 27

Two methods for combining results of multiple stochastic models

Answer 27

1. Run with same random variables, weight

2. Run with independent random variables, use cumulative distribution to pick

Question 28

Four reasons for fitting a curve to unpaid claim distributions

Answer 28

1. Asses quality of fit
2. Parameterize DFA model
3. Estimate extreme values
4. Estimate TVaR

Question 29

Kernel density functions

Answer 29

Can be fit to data to provide smoothed distribution to simulated results

Question 30

Two models for including correlation between bootstrap distributions for different business segments

Answer 30

Location mapping (within triangle)
Re-sorting (until rank correlation matches)