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

Author

Listed:
  • 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.

Suggested Citation

  • Wan-Kai Pang & Shui-Hung Hou & Marvin D. Troutt & Wing-Tong Yu & Ken W. K. Li, 2007. "A Markov Chain Monte Carlo Approach to Estimate the Risks of Extremely Large Insurance Claims," International Journal of Business and Economics, College of Business and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 6(3), pages 225-236, December.
  • Handle: RePEc:ijb:journl:v:6:y:2007:i:3:p:225-236
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    References listed on IDEAS

    as
    1. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(01), pages 71-92, May.
    2. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    heavy-tail distributions; loss distribution model; Pareto probability distribution; Gibbs sampler;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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