A Stochastic Planning Model for the Insurance Corporation of British Columbia

A stochastic planning model is a representation to an appropriate level of detail of all of the cash flows of an insurance company, where the variables are stochastic (randomly generated). The variables are connected by simple econometric equations whose form and parameters are generated by the relevant underlying data. The main virtue of stochastic planning models is that all the probability levels, and not just the mean, are available for any financial variable. Such a model has been built for a large Canadian automobile carrier, with the primary application to surplus requirements under different management decisions.

Although it is considerably more complex than the spreadsheet approach to risk-based capital being proposed by the NAIC, a stochastic model gives surplus requirements as a function of both appetite and management scenarios. The data and analysis requirements for a detailed model are substantial.

One of the by-products is a model of stochastic loss development involving accident period, development period, and payment period changes. Taken with the stochastic investment treatment and a projected zero future premium income, the run-off position variability can be quantified; i.e. the distribution of the adequacy of loss reserves can be ascertained.