Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis

Abstract

In actuarial practice, the modeling of total losses tied to a certain policy is a nontrivial task due to complex distributional features. In the recent literature, the application of the Dirichlet process mixture for insurance loss has been proposed to eliminate the risk of model misspecification biases. However, the effect of covariates as well as missing covariates in the modeling framework is rarely studied. In this article, we propose novel connections among a covariate-dependent Dirichlet process mixture, log-normal convolution, and missing covariate imputation. As a generative approach, our framework models the joint of outcome and covariates, which allows us to impute missing covariates under the assumption of missingness at random. The performance is assessed by applying our model to several insurance datasets of varying size and data missingness from the literature, and the empirical results demonstrate the benefit of our model compared with the existing actuarial models, such as the Tweedie-based generalized linear model, generalized additive model, or multivariate adaptive regression spline.

Keywords

• Bayesian nonparametric model
• heterogeneity
• missing at random
• log-normal sum approximation
• aggregate insurance claims
• clustering