Bivariate Distribution Regression with Application to Insurance Data

TL;DR

This paper introduces a semiparametric estimation method for modeling the conditional joint distribution of bivariate outcomes based on covariates, useful for risk analysis in insurance and other fields.

Contribution

It develops a flexible, semiparametric approach that handles discrete, continuous, or mixed variables without global parametric assumptions, improving dependence modeling.

Findings

Method performs comparably or better than existing approaches in simulations.

Effectively estimates risk measures like Value-at-Risk and Expected Shortfall.

Applicable to insurance data for risk management.

Abstract

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given observed circumstances. This article presents an estimation method for modeling the conditional joint distribution of bivariate outcomes based on the distribution regression and factorization methods. This method is considered semiparametric in that it allows for flexible modeling of both the marginal and joint distributions conditional on covariates without imposing global parametric assumptions across the entire distribution. In contrast to existing parametric approaches, our method can accommodate discrete, continuous, or mixed variables, and provides a simple yet effective way to capture distributional dependence structures between 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-party liability insurance portfolio, the proposed method effectively estimates risk measures such as the conditional Value-at-Risk and Expected Shortfall. This result suggests that this semiparametric approach can serve as an alternative in insurance risk management.