Title: Nonparametric copula estimation for mixed insurance claim data
Authors: Lu Yang - University of Amsterdam (Netherlands) [presenting]
Abstract: Multivariate claim data are common in insurance applications, e.g. claims of each policyholder from different insurance coverages. Understanding the dependencies of such multivariate risks is essential for the solvency and profitability of insurers. However, at the policyholder level, claim outcomes usually follow a hybrid distribution with a large point mass at zero corresponding to the case of no claims, while some customers report positive claims. In order to accommodate complex features of the marginal distributions while flexibly quantifying the dependencies among multivariate claims, we employ copulas. Although a substantial literature focusing on copula models with continuous outcomes has emerged, some key steps do not carry over to mixed data. In particular, existing nonparametric copula estimators are not consistent for mixed data. Thus, copula specification and diagnostics with mixed outcomes has remained a problem. We fill in this gap by developing a nonparametric copula estimator for mixed data. We show the uniform convergence of the proposed nonparametric copula estimator, and through simulation studies, we demonstrate that the probabilities of zero play a crucial role for the finite sample performance of the proposed estimator. Using the claim data from the Wisconsin Local Government Property Insurance Fund, we illustrate that our nonparametric copula estimator can assist analysts in identifying important features of the underlying dependence structure.