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題名 利用預測分析-篩選及檢視再保險契約中之承保風險
Selecting and Monitoring Insurance Risk on Reinsurance Treaties Using Predictive Analysis作者 吳家安
Wu, Chiao-An貢獻者 張士傑
Chang, Shih-Chieh
吳家安
Wu, Chiao-An關鍵詞 預測分佈
簡單重點重複抽樣法
蒙地卡羅模擬
吉普生抽樣法
比例再保險契約
超額損失再保險契約
Predictive distribution
Simple Importance-Resampling
Monte Carlo simulation
Gibbs sampling
Pro rata
Excess of loss日期 1998 上傳時間 27-四月-2016 16:43:10 (UTC+8) 摘要 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。
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.
Abstract i 1. Introduction.........7 1.1 Literatures Reviews and Preliminary.........8 1.2 Reinsurance Prior.........14 1.3 Loss Distribution and Credibility issue in insurance financing.........16 2. Predictive Distribution in Reinsurance Treaties.........19 2.1 Define Predictive Distribution.........19 2.2 Define Pro Rata and Excess-of-loss Reinsurance Treaties.........21 3. Review of Non-Bayesian and Bayesian Analyses.........24 3.1 Non-Bayesian Approach (Frequency result).........24 3.1.1 Confidence regions for future realizations.........24 3.1.2 Maximum likelihood predicting density (MLPD).........25 3.2 Bayesian Approach.........26 3.2.1 Simple Importance-Resampling (SIR) Scheme.........28 3.2.2 Monte Carlo Integration.........30 3.2.3 Markov chain Monte Carlo Method (Gibbs sampler).........33 4. Model Construction and Numerical Illustration.........36 4.1 Modeling Processes.........37 4.2 Numerical Illustration:A case study of catastrophe protection.........38 4.3 Sampling Techniques.........46 4.4 Convergence of the Risk Parameters.........47 4.5 Predictive Loss Distribution.........49 4.6 Underwriting Process in Monitoring the Retention Risks.........53 5. Conclusion and Comments.........59 5.1 Summary and comments.........59 5.2 Future works.........60 Appendix.........64 References.........61參考文獻 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. 描述 碩士
國立政治大學
應用數學系
86751009資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002001688 資料類型 thesis dc.contributor.advisor 張士傑 zh_TW dc.contributor.advisor Chang, Shih-Chieh en_US dc.contributor.author (作者) 吳家安 zh_TW dc.contributor.author (作者) Wu, Chiao-An en_US dc.creator (作者) 吳家安 zh_TW dc.creator (作者) Wu, Chiao-An en_US dc.date (日期) 1998 en_US dc.date.accessioned 27-四月-2016 16:43:10 (UTC+8) - dc.date.available 27-四月-2016 16:43:10 (UTC+8) - dc.date.issued (上傳時間) 27-四月-2016 16:43:10 (UTC+8) - dc.identifier (其他 識別碼) B2002001688 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/86783 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 86751009 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.abstract (摘要) Abstract i 1. Introduction.........7 1.1 Literatures Reviews and Preliminary.........8 1.2 Reinsurance Prior.........14 1.3 Loss Distribution and Credibility issue in insurance financing.........16 2. Predictive Distribution in Reinsurance Treaties.........19 2.1 Define Predictive Distribution.........19 2.2 Define Pro Rata and Excess-of-loss Reinsurance Treaties.........21 3. Review of Non-Bayesian and Bayesian Analyses.........24 3.1 Non-Bayesian Approach (Frequency result).........24 3.1.1 Confidence regions for future realizations.........24 3.1.2 Maximum likelihood predicting density (MLPD).........25 3.2 Bayesian Approach.........26 3.2.1 Simple Importance-Resampling (SIR) Scheme.........28 3.2.2 Monte Carlo Integration.........30 3.2.3 Markov chain Monte Carlo Method (Gibbs sampler).........33 4. Model Construction and Numerical Illustration.........36 4.1 Modeling Processes.........37 4.2 Numerical Illustration:A case study of catastrophe protection.........38 4.3 Sampling Techniques.........46 4.4 Convergence of the Risk Parameters.........47 4.5 Predictive Loss Distribution.........49 4.6 Underwriting Process in Monitoring the Retention Risks.........53 5. Conclusion and Comments.........59 5.1 Summary and comments.........59 5.2 Future works.........60 Appendix.........64 References.........61 - dc.description.tableofcontents Abstract i 1. Introduction.........7 1.1 Literatures Reviews and Preliminary.........8 1.2 Reinsurance Prior.........14 1.3 Loss Distribution and Credibility issue in insurance financing.........16 2. Predictive Distribution in Reinsurance Treaties.........19 2.1 Define Predictive Distribution.........19 2.2 Define Pro Rata and Excess-of-loss Reinsurance Treaties.........21 3. Review of Non-Bayesian and Bayesian Analyses.........24 3.1 Non-Bayesian Approach (Frequency result).........24 3.1.1 Confidence regions for future realizations.........24 3.1.2 Maximum likelihood predicting density (MLPD).........25 3.2 Bayesian Approach.........26 3.2.1 Simple Importance-Resampling (SIR) Scheme.........28 3.2.2 Monte Carlo Integration.........30 3.2.3 Markov chain Monte Carlo Method (Gibbs sampler).........33 4. Model Construction and Numerical Illustration.........36 4.1 Modeling Processes.........37 4.2 Numerical Illustration:A case study of catastrophe protection.........38 4.3 Sampling Techniques.........46 4.4 Convergence of the Risk Parameters.........47 4.5 Predictive Loss Distribution.........49 4.6 Underwriting Process in Monitoring the Retention Risks.........53 5. Conclusion and Comments.........59 5.1 Summary and comments.........59 5.2 Future works.........60 Appendix.........64 References.........61 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001688 en_US dc.subject (關鍵詞) 預測分佈 zh_TW dc.subject (關鍵詞) 簡單重點重複抽樣法 zh_TW dc.subject (關鍵詞) 蒙地卡羅模擬 zh_TW dc.subject (關鍵詞) 吉普生抽樣法 zh_TW dc.subject (關鍵詞) 比例再保險契約 zh_TW dc.subject (關鍵詞) 超額損失再保險契約 zh_TW dc.subject (關鍵詞) Predictive distribution en_US dc.subject (關鍵詞) Simple Importance-Resampling en_US dc.subject (關鍵詞) Monte Carlo simulation en_US dc.subject (關鍵詞) Gibbs sampling en_US dc.subject (關鍵詞) Pro rata en_US dc.subject (關鍵詞) Excess of loss en_US dc.title (題名) 利用預測分析-篩選及檢視再保險契約中之承保風險 zh_TW dc.title (題名) Selecting and Monitoring Insurance Risk on Reinsurance Treaties Using Predictive Analysis en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 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. zh_TW
