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| Volume 6, No. 3,
December
2007 |
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A Markov Chain Monte Carlo
Approach to Estimate the Risks of Extremely Large Insurance Claims |
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| Wan-Kai
Pang |
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Department of Applied Mathematics, The
Hong Kong Polytechnic University, Hong Kong |
| Shui-Hung
Hou |
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Department of Applied Mathematics, The
Hong Kong Polytechnic University, Hong Kong |
| Marvin D.
Troutt |
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Department of Management and
Information Systems, Kent State University, U.S.A. |
| Wing-Tong
Yu |
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School of Accounting and Finance, The
Hong Kong Polytechnic University, Hong Kong |
| Ken W. K.
Li |
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Department of Information and
Communications Technology, The Hong Kong Institute of Vocational
Education, Hong Kong |
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| Abstract |
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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. |
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Key words:
heavy-tail distributions; loss distribution model; |
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Pareto probability distribution; Gibbs sampler |
| JEL
classification:
C0; C1; G22 |
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