Volume 6, No. 3, December 2007

 

A Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims

Wan-Kai Pang
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
Shui-Hung Hou
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
Marvin D. Troutt
Department of Management and Information Systems, Kent State University, U.S.A.
Wing-Tong Yu
School of Accounting and Finance, The Hong Kong Polytechnic University, Hong Kong
Ken W. K. Li
Department of Information and Communications Technology, The Hong Kong Institute of Vocational Education, Hong Kong
Abstract

The Pareto distribution is a heavy-tailed distribution often used in actuarial models. It is important for modeling losses in insurance claims, especially when we used it to calculate the probability of an extreme event. Traditionally, maximum likelihood is used for parameter estimation, and we use the estimated parameters to calculate the tail probability Pr(X>c) where c is a large value. In this paper, we propose a Bayesian method to calculate the probability of this event. Markov Chain Monte Carlo techniques are employed to calculate the Pareto parameters.

Key words: heavy-tail distributions; loss distribution model;

Pareto probability distribution; Gibbs sampler

JEL classification: C0; C1; G22

Back