Knowledge Learning of Insurance Risks Using Dependence Models

Learning the customers' experience and behavior creates competitive advantages for any company over its rivals. The insurance industry is an essential sector in any developed economy and a better understanding of customers' risk profile is critical to decision making in all aspects of insurance operations. In this paper, we explore the idea of using copula-based dependence models to learn the hidden risk of policyholders in property insurance. Specifically, we build a novel copula model to accommodate the dependence over time and over space among spatially clustered property risks. To tackle the computational challenge caused by the discreteness feature of large-scale insurance data, we propose an efficient multilevel composite likelihood approach for parameter estimation. Provided that latent risk induces correlation, the proposed customer learning method offers improved predictive analytics by allowing insurers to borrow strength from related risks in predicting new risks and also helps reveal the relative importance of the multiple sources of unobserved heterogeneity in updating policyholders' risk profile. In the empirical study, we examine the loss cost of a portfolio of entities insured by a government property insurance program in Wisconsin. We find both significant temporal and spatial association among property risks. However, their effects on the predictive distribution of loss cost are different for the new and renewal policyholders. The two sources of dependence are complements for the former and substitutes for the latter. These findings are shown to have substantial managerial implications in key insurance operations such as experience rating, capital allocation, and reinsurance arrangement.