风险约束下的最优保险合约设计

发布时间：2018-03-03 14:46

  本文选题：最优保险　切入点：风险约束　出处：《南京大学》2017年硕士论文　论文类型：学位论文

【摘要】：目前我国的经济发展步入新常态,面对"三期叠加"的挑战,保险业却依旧保持两位数的高速发展。在保险行业蓬勃发展的同时,以风险为导向的"偿二代"监管体系对保险公司的风险防范能力也提出了更高的要求。保险公司需要进行必要的研究提高风险管理能力以适应这种新变化,推动和深化保险领域市场化改革。在保险业风险管理当中,合同设计是最为重要的环节,关于"最优保险"合约设计的问题越来越得到重视。目前关于最优保险的学术研究主要是针对被保险人,即最大化被保险人的期望效用,从而获得不同保费计算原理下的最优保险形式,但是很少有学术研究关注保险公司的外在风险,所以保险公司在设计最优保险合约的过程中既要考虑被保险人的财富效用最大化,又要将保险人未来可能发生的风险控制在一定范围内,不断完善自身的风险管理能力。本文以被保险人的期望效用最大化为规划目标,介绍和探讨了关于保险人在风险约束下的最优保险合约设计问题。本文分为六章,第一章为绪论,首先介绍了本文研究的背景和保险及其相关的预期基本效能指标和风险态度的基本概念,概述了关于最优保险合约设计相关理论的研究结果,并做进一步探讨。本文在被保险人期望效用最大化的规划目标下对保险人分别添加了三类风险约束条件,即在被保险人期望终值财富最大化的目标下,也要将保险公司未来可能发生的风险控制在一定范围内。第二章中对保险人的风险约束条件采用约束破产概率的形式,第三章中将保险的外在期望损失控制在一定的容忍度之内,对于保险人的风险约束条件采用期望的形式,第四章中对保险人的风险约束条件采用约束绝对最大损失的形式。之前的研究仅考虑了单一的风险约束条件,所以本文的创新之处在于在这三章的约束条件中均同时考虑了保险人的承保风险和投资风险,分别在此规划目标下建立相应的数理模型,并对模型进行详细的分析讨论,同时对模型的结果做出经济学意义的解释。第五章中介绍了三个简单的模型算例来说明前三章得出的结论并进行了比较,同时将本文最优保险的模型应用于车险市场和医疗保险市场的实际情况进行说明。最后本文得出结论是在Var风险约束模型下,保险人不仅会增加对被保险人小额损失的赔偿,也会增加对被保险人大额损失的赔偿,当发生大额风险时,保险人的风险暴露最大。在期望损失风险约束模型下,保险人会增加对被保险人小额损失的赔偿,减少对被保险人大额损失的赔偿,相对破产概率风险约束模型,保险人的风险暴露要严格一些。与此同时,如果Arrow模型的解满足保险人的风险约束条件,保险人的风险容忍度增加对被保险人的期望效用没有影响,如果Arrow模型的解不满足保险人的风险约束条件,且存在最优解,则保险人的风险容忍度增加,被保险人的期望效用也会增加。在约束保险人绝对最大损失风险的模型下,保险人加大对被保险人可能发生的小额损失进行补偿,但是不会对超过最高保险额度以上的损失进行赔偿,即保险人只会在保额限度之内对被保险人所发生的费用进行赔偿,超过保险金额限度的部分保险人不予以赔偿。显然可以看出,保险人绝对最大损失风险约束模型比保险人期望损失风险约束模型和保险人破产概率模型更符合现实,与此同时,由于被保险人无法将大额度损失转移出去也降低了被保险人的期望效用。
[Abstract]:At present, China's economic development has entered a new norm, facing three overlay challenges, the insurance industry still maintained rapid development of two digit. In the vigorous development of the insurance industry at the same time, the risk oriented compensation two generation "supervision system of insurance company risk prevention capability is also put forward higher requirements the insurance company requires the necessary research to improve the risk management ability to adapt to the new changes, to promote and deepen the field of insurance market reform. In the risk management of insurance industry, the contract design is the most important part, questions about" the optimal insurance contract gets more and more attention. The current academic research on the optimal insurance mainly for the insured, the insured is to maximize the expected utility, to obtain different forms under the principle of optimal insurance premium calculation, but there is little academic research insurance company outside In the risk, so the insurance company in the process of designing the optimal insurance contracts should not only take into account the maximum insured wealth utility, and risk insurance possible future control in a certain range, and constantly improve their risk management ability. This paper is to maximize the insurer's expected utility for planning objectives, introduction and the discussion about the optimal insurance contract design problem in the risk under the constraint of the insurer. This paper is divided into six chapters, the first chapter is the introduction, first introduced the basic concepts and the background of this study and the expected effectiveness index of basic insurance related and risk attitude, the research results about the optimal insurance contract design theory overview and do the further study in this article. The insured expected utility maximization under the planning objectives of the insurance were added to three kinds of risk constraints, namely the insured period At the final wealth maximization goal, will risk insurance companies in the future may occur within a certain range. The constraint of ruin probability in the form of risk constraints for the insurer in the second chapter, the third chapter will be the external insurance expected loss control in a certain degree of tolerance, to expect in the form of insurance the risk constraint, constraint absolute maximum loss in the form of risk constraints for the insurer in the fourth chapter. Previous studies only consider single risk constraints, so the innovation of this paper lies in the three chapter, the constraints are considered at the same time, the underwriting of insurance risk and investment risk, establish the corresponding mathematical model of the planning target respectively, and the model is discussed in detail, and make an economic model significance for the interpretation of the results. The fifth chapter intermediary Introduces three simple model examples show that the first three chapters and the conclusion were compared, and the application of this model the optimal insurance in the auto insurance market and the actual situation of the medical insurance market is described. Finally, the conclusion is in Var risk constraint model, the insurer will not only increase the insured one small losses, will also increase the insured for large losses when a large risk, the risk of the insurer. In the exposure maximum expected loss risk constraint model, the insurer will increase the insured for small losses, reduce the insured large losses, the probability of risk the relative risk constraint model of bankruptcy, the insurer's exposure to strictly. At the same time, if the insurer's risk constrained solutions of Arrow model, the insurer's risk tolerance of the insured No effect of expected utility, if the solution of the Arrow model does not meet the insurance risk constraints, and the optimal solution exists, the risk tolerance of the insurer increases, the insured's expected utility will increase. In the constraint insurer absolute maximum loss risk model, the insurer for compensation of losses is small increase the insurer may occur, but not the compensation for more than the highest amount of insurance loss, the insurer will only be incurred to compensate the insurers in the coverage limit, more than part of the insurance amount is not compensation. It is evident that the insurance risk constraint model than the absolute maximum loss the insurer expected loss risk constraint model and insurance ruin probability model is more consistent with the reality, at the same time, because the insured cannot be transferred out large amount loss also reduced The expected utility of the insured.

【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F842.6
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本文编号：1561482