A Statistical Basis for Claims Experience Monitoring

By claims experience monitoring is meant the systematic comparison of the forecasts from a claims model with claims experience as it emerges subsequently. In the event that the stochastic properties of the forecasts are known, the comparison can be represented as a collection of probabilistic statements. This is stochastic monitoring. This paper defines this process rigorously in terms of statistical hypothesis testing. If the model is a regression model (which is the case for most stochastic claims models), then the natural form of hypothesis test is a number of likelihood ratio tests, one for each parameter in the valuation model. Such testing is shown to be very easily implemented by means of generalized linear modeling software. This tests the formal structure of the claims model and is referred to as microtesting. There may be other quantities (e.g., amount of claim payments in a defined interval) that require testing for practical reasons. This sort of testing is referred to as macrotesting, and its formulation is also discussed.