Bivariate Distribution Regression with Application to Insurance Data

Abstract

This article introduces an estimation method for the conditional joint distribution of bivariate outcomes, based on the distribution regression approach and the factorization method. The proposed method can apply for discrete, continuous or mixed distribution outcomes. It is semiparametric in that both marginal and joint distributions are left unspecified, conditional on covariates. Unlike the existing parametric approaches, our method is simple yet flexible to encapsulate distributional dependence structures of bivariate outcomes and covariates. Various simulation results confirm that our method can perform similarly or better in finite samples compared to the alternative methods. In an application to the study of a motor third-part liability insurance portfolio, the proposed method effectively captures key distributional features in the data, especially the value at risks conditional on covariates. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.