变量变换和MIF函数下的最优再保险
发布时间：2019-06-06 05:27
【摘要】：再保险是保险公司的一个有效风险管理工具,保险公司通过平衡分出损失和再保险保费,将部分风险转移到再保险公司来控制其风险.衡量最优再保险的常见标准可以分为以下三类:方差最小化、效用函数最大化以及破产概率最小.近几年,许多学者应用风险度量来研究最优再保险.因此,我们通过风险度量来研究最优性再保险策略.主要内容概述如下:第一章,介绍了再保险的研究背景、研究现状以及本文的研究内容.第二章,介绍了再保险的定义、常见的保费原理及风险度量.第三章,我们以停止-损失再保险作为研究对象.在和风险度量下,提出了一个变量变换方法分别得到了和风险度量下停止损失再保险的最优自留额.假设是保险人的初始损失,对应的累计分布函数为(3()=((3≤)并且生存函数为.记变换为,首先,分析了变量和的性质.然后,在VaR和CTE最优化标准下,我们给出了对应自留额存在的充分必要条件.最后,得到对应的最优自留额.给出一些例子对以上的结果进行说明.第四章,考虑了再保险人违约风险的影响,研究了在风险度量下的最优再保险.在再保险合同中,再保险人承诺支付保险人面临的部分损失通过向保险人收取一定的保费.然而,当再保险人承诺支付的限额超过了他自己的偿付能力,则违约风险发生.因此考虑了违约风险并且对再保险人的初始资本进行一定的限定是必要的.在(2(69)2)′保费原理下,应用风险度量VaR的最优化标准使得保险人的总风险最小得到分层再保险是最优的.最后,给出相应的数值算例.第五章,应用扭曲风险度量和扭曲保费原理建立了含有违约风险的总风险模型.首先,通过边际索赔(MIF)函数与分出函数之间的关系建立了与总风险模型等价的MIF再保险优化模型.然后对MIF再保险优化模型的求解得到最优的边际索赔(MIF)函数,进而得到最优的分出函数.最后,应用该方法研究了在VaR风险度量和Wang’s保费原理下的最优分出函数.第六章,对本文的研究结果进行了讨论和总结.
[Abstract]:Reinsurance is an effective risk management tool for insurance companies. By balancing losses and reinsurance premiums, insurance companies transfer some of the risks to reinsurance companies to control their risks. The common criteria for measuring optimal reinsurance can be divided into the following three categories: minimum variance, maximization of utility function and minimum ruin probability. In recent years, many scholars use risk measurement to study optimal reinsurance. Therefore, we study the optimal reinsurance strategy through risk measurement. The main contents are summarized as follows: the first chapter introduces the research background of reinsurance, the research status and the research content of this paper. The second chapter introduces the definition of reinsurance, the common premium principle and risk measurement. In the third chapter, we take stop-loss reinsurance as the research object. Under the condition of sum risk measurement, a variable transformation method is proposed to obtain the optimal retention amount of stop loss reinsurance under and risk measurement, respectively. Suppose it is the initial loss of the insurer, the corresponding cumulative distribution function is (3 () = (3 鈮，
本文编号：2494105
[Abstract]:Reinsurance is an effective risk management tool for insurance companies. By balancing losses and reinsurance premiums, insurance companies transfer some of the risks to reinsurance companies to control their risks. The common criteria for measuring optimal reinsurance can be divided into the following three categories: minimum variance, maximization of utility function and minimum ruin probability. In recent years, many scholars use risk measurement to study optimal reinsurance. Therefore, we study the optimal reinsurance strategy through risk measurement. The main contents are summarized as follows: the first chapter introduces the research background of reinsurance, the research status and the research content of this paper. The second chapter introduces the definition of reinsurance, the common premium principle and risk measurement. In the third chapter, we take stop-loss reinsurance as the research object. Under the condition of sum risk measurement, a variable transformation method is proposed to obtain the optimal retention amount of stop loss reinsurance under and risk measurement, respectively. Suppose it is the initial loss of the insurer, the corresponding cumulative distribution function is (3 () = (3 鈮，
本文编号：2494105
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