A Flexible Bayesian Nonparametric Model for Predicting Future Insurance Claims
21 Pages Posted: 16 Nov 2015 Last revised: 5 Nov 2016
Date Written: July 21, 2016
Accurate prediction of future claims is a fundamentally important problem in insurance. The Bayesian approach is natural in this context, as it provides a complete predictive distribution for future claims. The classical credibility theory provides a simple approximation to the mean of that predictive distribution as a point-predictor, but this approach ignores other features of the predictive distribution, such as spread, that would be useful for decision-making. Unfortunately, these other features are more sensitive to the choice of loss model and prior distribution, so a flexible nonparametric Bayesian model is desirable. In this paper, we propose a Dirichlet process mixture of log-normals model and discuss the theoretical properties and computation of the corresponding predictive distribution. Numerical examples demonstrate the benefit of our model compared to some existing insurance loss models.
Keywords: Credibility theory; density estimation; Dirichlet process; Markov chain Monte Carlo; mixture model; posterior consistency.
JEL Classification: C14, C15, G22
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