Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

Minwoo Kim, Himchan Jeong and Dipak Dey
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Minwoo Kim: Department of Statistics and Probability, Michigan State University, Wells Hall 619 Red Cedar Road, East Lansing, MI 48824, USA
Himchan Jeong: Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada
Dipak Dey: Department of Statistics, University of Connecticut, 215 Glenbrook Rd. U-4120, Storrs, CT 06269, USA

Risks, 2022, vol. 10, issue 3, 1-11

Abstract: While both zero-inflation and the unobserved heterogeneity in risks are prevalent issues in modeling insurance claim counts, determination of Bayesian credibility premium of the claim counts with these features are often demanding due to high computational costs associated with a use of MCMC. This article explores a way to approximate credibility premium for claims frequency that follows a zero-inflated Poisson distribution via variational Bayes approach. Unlike many existing industry benchmarks, the proposed method enables insurance companies to capture both zero-inflation and unobserved heterogeneity of policyholders simultaneously with modest computation costs. A simulation study and an empirical analysis using the LGPIF dataset were conducted and it turned out that the proposed method outperforms many industry benchmarks in terms of prediction performances and computation time. Such results support the applicability of the proposed method in the posterior ratemaking practices.

Keywords: approximate credibility premium; claim frequency; posterior ratemaking; variational Bayes; zero-inflated Poisson distribution (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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