Mildenhall Aggregate Loss Tools

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Example 7: Create Aggregate Loss Distribution

Notes

• Specify either the contagion or variance multiplier to determine the variance of the frequency distribution.
• For a negative binomial distribution with mean m, the variance is vm for a variance multiplier v and m(1+cm) for a contagion of c.
• Specify the severity either using a built-in curve from the list or input your own parameters. (Note: since ISO parameters are proprietary, all the built-in distributions in the sample are the same "reasonable" distribution. See the Appendix for information on building your own parameter file, to incorporate your own proprietary data.)
• For user defined distributions, input the parameters in the appropriate text boxes.
• The shifted lognormal is T + lognormal(mu, sigma). If T=0 this is a standard lognormal distribution.
• The Pareto distribution is parameterized as in Wang, Appendix A.
• Model shows plots of the aggregate distribution, a comparison of lognormal and shifted lognormal fits to the aggregate, the severity distribution and the frequency distribution.
• Model also shows mean, CV and skewness for the frequency, severity and aggregate distributions, as well as the shifted-lognormal parameters for the aggregate.
• Try a small claim count to see and interesting, discontinuous aggregate. Why is it discontinuous?

References to Wang

• This is the main method of Section 3.3.1.
• Num_l2 is what Wang calls r.
• Appendix A.