Modeling the "pseudodeductible" in insurance claims decisions

In many different managerial contexts, consumers "leave money on the table" by, for example, their failure to claim rebates, use available coupons, and so on. This project focuses on a related problem faced by homeowners who may be reluctant to file insurance claims despite the fact their losses are covered. We model this consumer decision by introducing the concept of the "pseudodeductible," a latent threshold above the policy deductible that governs the homeowner's claim behavior. In addition, we show how the observed number of claims can be modeled as the output of three stochastic processes that are separately, and in conjunction, managerially relevant: the rate at which losses occur, the size of each loss, and the choice of the individual to file or not file a claim. By allowing for the possibility of pseudodeductibles, one can sort out (and make accurate inferences about) these three processes. We test this model using a proprietary data set provided by State Farm, the largest underwriter of personal lines insurance in the United States. Using mixtures of Dirichlet processes to capture heterogeneity and the interplay among the three processes, we uncover several relevant "stories" that underlie the frequency and severity of claims. For instance, some customers have a small number of losses, but all are filed as claims, whereas others may experience many more losses, but are more selective about which claims they file. These stories explain several observed phenomena regarding the claims decisions that insurance customers make, and have broad implications for customer lifetime value and market segmentation.