Shapland and Leong Flashcards
Two advantages of bootstrapping
1) Allow us to calculate likelihood that claims will exceed certain amount
2) Able to reflect skewness of insurance losses
One disadvantage of bootstrapping
More complex and time consuming
How using ODP relates GLM to standard CL
Start with latest diagonal and divide backwards to obtain fitted incrementals
Three important outcomes from using ODP to relate GLM to standard CL
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
Assumptions underlying residual sampling process
Residuals are iid
Two uses of degrees of freedom adjustment factor
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
Downfall of degrees of freedom adjustment factor
Does not create standardized residuals
Benefit of bootstrapping incurred triangle
Leverages case reserves to better predict ultimate claims
One deterministic method for reducing variability in extrapolation of future incremental values
BF method
Four advantages to generalizing ODP
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
Two disadvantages to generalizing ODP
GLM must be solved for each iteration; time-consuming
Disadvantage to including CY trends in ODP/remedy
GLM no longer has a unique solution/start with a single parameter and add as needed
Four options for dealing with negative incremental values in ODP
1) Remove extreme iterations
2) Recalibrate model
3) Limit incrementals to zero
4) Use more than one model
Why average of residuals from ODP may differ from zero in practice
Different AYs develop at different rates relative to weighted average
Arguments for and against adjusting residuals to average to zero
For: re-sampling adds variability to resampled incremental losses
Against: It is a characteristic of the data set
How to adjust residuals of ODP to overall mean of zero
Add single constant to all residuals such that sum of shifted residuals is zero
Three approaches to managing missing values in triangle
- Exclude
- Estimate using surrounding values
- If missing value lies on last diagonal, use value in second to last diagonal to construct fitted triangle
Three approaches to managing outliers in the loss triangle
- If on first row, we can delete row
- Exclude completely
- Exclude when calculating LDFs but re-sample
Difference between homoscedastic and heteroscedastic residuals
Homo - residuals are iid
Hetero - independent but not independently distributed
Two options to adjust residuals for heteroscedasticity
Stratified Sampling Variance parameters (hetero-adjustment factors)
Interaction between heteroscedasticity and credibility
Important not to overact to apparent heteroscedasticity in older development years
Heteroechtesious data
Incomplete or uneven exposures at interim evaluation dates
Two types of heteroecthesious data
Partial first development period (first column has different exposure period than rest of column)
Partial last calendar period data (six month diagonal)
Diagnostic tests to assess quality of stochastic model
- Test assumptions in model
- Gauge quality of model fit
- Guide adjustment of model parameters
Red flags in an output from bootstrap model
- Standard errors should increase over time
- Reserves should be increasing over time
- CoV should decrease over time
- Total standard error should be larger than any individual AY
Two reasons why CoV may rise in most recent AYs
Increasing parameter uncertainty
Simple overestimation of recent variability
Two methods for combining results of multiple stochastic models
- Run with same random variables, weight
2. Run with independent random variables, use cumulative distribution to pick
Four reasons for fitting a curve to unpaid claim distributions
- Asses quality of fit
- Parameterize DFA model
- Estimate extreme values
- Estimate TVaR
Kernel density functions
Can be fit to data to provide smoothed distribution to simulated results
Two models for including correlation between bootstrap distributions for different business segments
Location mapping (within triangle) Re-sorting (until rank correlation matches)
