A Copula Approach To Test Asymmetric Information with Applications to Predictive Modeling
Emiliano A. Valdez1, Peng Shi2
1Department of Mathematics, University of Connecticut, Storrs, CT, United States; 2Division of Statistics, Northern Illinois University, DeKalb, IL, United States

In our paper, we provide an alternative evidence of asymmetric information in automobile insurance based on a copula model. We use the Frank's copula to jointly model the type of policy coverage chosen and the number of accidents, with the dependence parameter providing for evidence of the relationship between the choice of coverage and the frequency of accidents. This dependence therefore provides an indication of the presence (or absence) of asymmetric information. The type of coverage is in some sense ordered so that coverage with higher ordinals indicates the most comprehensive coverage. Henceforth, a positive relationship would indicate that more coverage is chosen for those with higher frequency of accidents, and vice versa. This presence of asymmetric information could be due to either adverse selection or moral hazard, a distinction often made in the economics of insurance literature, or both. We calibrated our copula model using a one-year cross-sectional observation of claims arising from a major automobile insurer in Singapore. Our estimation results indicate a strong evidence of the presence of asymmetric information, and we further used our estimated model for other possible actuarial applications. In particular, we are able to demonstrate the effect of coverage choice on the incidence of accidents, and based on which, a posterior pure premium is derived. In general, a positive margin is observed when compared with a prior premium available in our empirical database.

Keywords: Adverse selection; Moral hazard; Copula models; Predictive models

Biography: Emiliano (Emil) A. Valdez, Ph.D, FSA, is a Professor of Actuarial Science in the Department of Mathematics at the University of Connecticut, USA. He is a Fellow of the Society of Actuaries and holds a Ph.D. from the University of Wisconsin in Madison. He has been awarded the Edward A. Lew Award, the Halmstad Memorial Prize, and recently in 2010, the Charles A. Hachemeister Prize, in recognition for his significant contributions to the actuarial literature. His current research interest includes copula models and dependencies, managing post-retirement assets, and risk measures and capital requirements related to enterprise risk management.