效用理论下最优再保险研究分析-毕业论文.docVIP

Dissertation Submitted to Hebei University of Technology for The Master Degree of Science in Applied Mathematics ON ANALYSIS OF OPTIMAL REINSURANCE RESEARCH UNDER UTILITY THEORY by Li Zhenhua Supervisor: Prof. Liu Guoxin November 2012 河北工业大学硕士学位论文 效用理论下最优再保险研究分析 摘 要 再保险是保险公司之间分散风险的一种重要交易方式, 对于稳定保险市场具有极为重要的意义. 最优再保险是再保险研究中的主要课题之一, 主要问题是在一定优化准则下, 保险人如何确定自留额 和再保险形式. 本文基于个体风险的最优再保险模型, 在效用理论下建立了最优再保险的推广模型. 一般基于个 体风险的效用理论模型中, 所采用的期望保费准则都为 P?? (1??? )E(R)(?  ? 0) . 本文在此基础上将 其保费条件推广, 建立了幂函数期望保费准则的最优再保险模型, 得出了最优自留额满足的方程及其 解存在的充分条件, 并通过实例分析验证了定理的正确性. 本文还在推广模型的基础上对再保险人所承担的风险进行了方差限制 , 对最优自留额的存在性及 其求解重新进行讨论, 并得出了相关结论. 最后将方差限制对保险人和再保险人的影响进行了详细的 分析, 也通过实例分析验证了结论的正确性. 关键词:  最优再保险, 个体风险, 效用理论, 自留额, 方差限制  i 效用理论下最优再保险研究分析 ON ANALYSIS OF OPTIMAL REINSURANCE RESEARCH UNDER UTILITY THEORY ABSTRACT As an important transaction to risk diversification amid insurance companies, reinsurance has a very important significance for the stability of the insurance market. Optimal reinsurance is one of the major topics in the study of reinsurance. Its main research topic is how to determine self-insured retention and the form of reinsurance for insurers under the certain optimization criteria. Based on the optimal reinsurance models for individual risks, the optimal reinsurance promotion model is established according to the utility theory. Among most utility theory model for individual risks, intended coverage is calculating in accordance with the criterion P?? (1???? )E (R ) (??? 0) . In this paper, premium conditions are promoted, which are including optimal reinsurance model of power-functional intended coverage criteria, the optimal self-insured retention equation and sufficient condition with its solution. And the correctness of the theorem is verified by examples. This paper also assumed the variance limit of risks undergone by reinsurers on the basis of the promoting model. The existence of the optimal self-insured retention has been additionally re-discussed to r