Kim, M.; Lindberg, D.; Crane, M.; Bezbradica, M. Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis. Econometrics2023, 11, 24.
Kim, M.; Lindberg, D.; Crane, M.; Bezbradica, M. Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis. Econometrics 2023, 11, 24.
Kim, M.; Lindberg, D.; Crane, M.; Bezbradica, M. Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis. Econometrics2023, 11, 24.
Kim, M.; Lindberg, D.; Crane, M.; Bezbradica, M. Dirichlet Process Log Skew-Normal Mixture with a Missing-at-Random-Covariate in Insurance Claim Analysis. Econometrics 2023, 11, 24.
Abstract
In actuarial practice, the modeling of total losses tied to a certain policy is a non-trivial task. Traditional parametric models to predict total losses have limitations due to complex distributional features such as extreme skewness, zero inflation, multi-modality, etc., and the lack of explicit solutions for log-normal convolution. 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 covariate-dependent Dirichlet process mixture, log-normal convolution, and missing covariate imputation. Assuming an individual loss is log-normally distributed, we develop a log skew-normal Dirichlet process to approximate the log-normal sum. As a generative approach, our framework models the joint of outcome and covariates, which allows to impute missing covariates under the assumption of missingness at random. The performance is assessed by applying our model to several insurance datasets, and the empirical results demonstrate the benefit of our model compared to 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; generative model
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
