傳統的保險人在面對保險契約所承保的風險時，常會藉由國際上的再保險市場來分散其保險風險。由於所承保險事件的不確定性，保險人需要謹慎小心評估其保險風險並將承保風險轉移至再保險人。再保險有兩種主要的保險型式，可區分成比例再保契約及超額損失再保契約，保險人將利用這些再保險契約來分散求償給付時的損失，加強保險人本身的財務清償能力。

本研究，主要在於建構未來損失求償幅度或頻率的預測分佈並模擬未來支付求償的損失。簡單重點重複抽樣法是一種從危險參數的驗後分佈中抽樣的抽樣方法。然而，蒙地卡羅模擬是一種利用大量電腦運算計算近似預測分佈的逼近方法。利用被選取危險參數的驗前分佈來模擬其驗後分佈，並建構可能的承保危險參數結構，將基於馬可夫鏈蒙地卡羅理論的吉普生抽樣方法決定最適自留額，同時運用於再保險合約決策擬定過程。

最後，考慮於不同的再保險契約下來衡量再保險人的自負財務風險。基本上我們研究的對象是針對保險人所承保的風險，再藉由上述的方法來模擬、近似以量化所衍生的財務風險。這將有助於保險人清楚地瞭解其承保的風險，並對其承保業務做妥善的財務風險管理。本研究提供保險人具體的模型建構方法並對此建構技巧做詳細說明及實證分析。

Insurers traditionally transfer their insurance risk through the international reinsurance market. Due to the uncertainty of these insured risks, the primary insurer need to carefully evaluate the insured risk and further transfer these risks to his ceding reinsurers. There are two major types of reinsurance, i.e. pro rata treaty and excess of loss treaty, used in protecting the claim losses.

In this article, the predictive distribution of the claim size is constructed to monitor the future claim underwriting losses based on the reinsurance agreement. Simple Importance Resampling (SIR) are employed in sampling the posterior distribution of risk parameters. Then Monte Carlo simulations are used to approximate the predictive distribution. Plausible prior distributions of these risk parameters are chosen in simulation its posterior distribution. Markov chain Monte Carlo (MCMC) method using Gibbs sampling scheme is also performed based on possible parametric structures. Both the pro rata and excess of loss treaties are investigated to quantify the retention risks of the ceding reinsurers.

The insurance risks are focused in our model. Through the implemented model and simulation techniques, it is beneficial for the primary insurer in projecting his underwriting risks. The results show a significant advantage and flexibility using this approach in risk management. This article outlines the procedure of building the model. Finally a practical case study is performed for numerical illustrated.

lan, E.G., Adrian, F.M., and Tai-Ming L., Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling, Journal of the American Statistical Association 87, 1992, pp.523-532.
Bowers, N., Gerber, H., Hickman, J., Jones, D. and Nesbitt, C., Actuarial Mathematics, Chicago: Society of Actuaries, 1986.
Buhlmann,H., Experience Rating and Credibility, ASTIN Bulltin 4, 1967, pp.199-207.
Buhlmann,H., Experience Rating and Credibility, ASTIN Bulltin 5, 1969, pp.157-165.
Buhlmann, H., and Straub, E., Credibility for Loss Ratios, English translation in ARCH, 1972.
Chang, S.C., Simple Bayes method in estimating the claim size of the insured risks, Insurance Monograph, 43, 1996, pp.160-165.
Chang, S.C., Using Monte Carlo Markov chain method to analyze the loss distributions under various risks, Insurance Monograph, 44, 1997, pp.40-51.
David, P.M., A Bayesian analysis of a simultaneous equations model for insurance rate-making, Insurance: Mathematics and Economics, 12, 1993, pp.265-286.
Daykin, C.D., T. and Pesonen, M., Practical Risk Theory for Actuauies, London: Chapman & Hall, Inc, 1994.
Geisser, S., Predictive Inference: An Introduction, London: Chapman & Hall, Inc, 1993.
Gilk, W. R., Markov Chain Monte Carlo in Practice, London: Chapman & Hall, Inc, 1996.
Gelfand, A.E., and Smith, A.F.M., Sampling based approaches to calculating matginal densities, Journal of the American Statistical Association, 85, 1990, pp.398-409.
Grandell, J., Aspects of Risk Theory, New York: Springer Verlag, Heidelberg, 1991.
Geyer, C.J., and Thompson, E.A. Annealing Markov chain Monte Carlo with applications to pedigree analysis, Journal of the American Statistical Association, 1995.
Hastings, W.K., Monte Carlo sampling methods using Markov chains and their applications, Biomebrika 57, 1970, pp.97-109.
Herzog, T., An Introduction to Bayesian Credibility and Related Topics, Part 4 Study Note, New York: Casualty Actuarial Society.
Hogg, R.V. and Klugman, S.A., Loss Distributions, New York: Wiley, 1984.
Huebner, S.S., Black, K. and Cline, R., PROPERTY AND LIABILITY INSURANCE, America: Prentice Hall, Inc, 1982.
James, O.B., and Ming-Hui C., Predicting retirement patterns: prediction for a multinomial distribution with constrained parameter space, The Statistician 42, 1993, pp.427-443.
Johnson, V.E., Studying Convergence of Markov Chain Monte Carlo Algorithms Using Coupled Sample Paths, Journal of the American Statistical Association 91, 1996, pp.155-166.
Klugman, S.A., Bayesian Statistics in Actuarial Science, America: Kluwer Academic Publishers, 1992.
Liu, C. H., Pricing for the catastrophic future option, unpublished master thesis, National Chengchi University, Department of Risk Management and Insurance, 1997.
Polson, N.G., Convergence of Markov chain Monte Carlo algorithms, Bayesian Statistic 5, Oxford: Oxford University Press, 1995.
Parmenter, M., Theory of Interest and Life Contingencies, with Pension Applications: A Problem Solving Approach, Winsted, CT: ACTEX, 1988.
Robert, C., THE BAYESIAN CHOICE, New York: Springer Verlag, Heidelberg, 1994.
Rubin, D. B., "Using the SIR Algorithm to Simulate Posterior Distributions," in Bayesian Statistics 3, eds. Bernardo, J. M., De Groot, M. H., Lindley, D. V., and Smith, A. F. M., New York: Oxford University Press, 1988.
S-PLUS Programmer's Manual, Version 3.3. StatSci, MathSoft Inc. Seattle, Washington, 1989.
Stewart, L.T., Hierarchical Bayesian analysis using Monte Carlo integration: computing posterior distributions when there are many possible models, The Statistician 36, 1987, pp.211-219.
Tierney, L., Exploring posterior distributions using Markov chains. Computer Science and Statistics, 1991, pp.563-570.
Tanner, M.A., and Wong, W.H., The calculation of posterior distributions by data augmentation, Journal of the American Statistical Association, 82, 1995, pp.528-540.
Van Dijk, H.K., Peter Hop, J., and Louter, A.S., An algorithm for the computation of posterior moments and densities using simple importance sampling, The Statistician 36, 1987, pp.83-90.