Dirichlet Process Mixture Models for Insurance Loss Data

13 Pages Posted: 11 Apr 2017 Last revised: 31 Oct 2017

See all articles by Liang Hong

Liang Hong

The University of Texas at Dallas

Ryan Martin

North Carolina State University - Department of Statistics

Date Written: October 31, 2017

Abstract

In the recent insurance literature, a variety of finite-dimensional parametric models have been proposed for analyzing the hump-shaped, heavy-tailed, and highly skewed loss data often encountered in applications. These parametric models are relatively simple, but they lack flexibility in the sense that an actuary analyzing a new data set cannot be sure that any one of these parametric models will be appropriate. As a consequence, the actuary must make a non-trivial choice among a collection of candidate models, putting him/herself at risk for various model misspecification biases. In this paper, we argue that, at least in cases where prediction of future insurance losses is the ultimate goal, there is reason to consider a single but more flexible nonparametric model. We focus here on Dirichlet process mixture models, and we reanalyze several of the standard insurance data sets to support our claim that model misspecification biases can be avoided by taking a nonparametric approach, with little to no cost, compared to existing parametric approaches.

Keywords: Danish Fire Losses Data; General Insurance; Model Misspecification; Nonparametric Bayes; Norwegian Fire Losses Data; Property and Casualty Insurance; U.S. Allocated Loss Adjustment Expenses Data

Suggested Citation

Hong, Liang and Martin, Ryan, Dirichlet Process Mixture Models for Insurance Loss Data (October 31, 2017). Available at SSRN: https://ssrn.com/abstract=2949036 or http://dx.doi.org/10.2139/ssrn.2949036

Liang Hong (Contact Author)

The University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Ryan Martin

North Carolina State University - Department of Statistics ( email )

Raleigh, NC 27695-8203
United States

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