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Dirichlet process mixture models for insurance loss data. (English) Zbl 1416.91188

Summary: 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62G07 Density estimation
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