再保险双方的联合鲁棒最优投资—再保险策略研究
发布时间：2018-07-15 07:09
【摘要】：保险公司的资产配置问题一直是保险精算领域的研究热点,其主要的配置方式包括再保险、投资、分红等。如何选择合理的投资、再保险策略,以分摊风险、稳定经营、提升保险公司的企业实力一直是保险精算学者的重要研究内容。20世纪70年代以来,对保险公司资产配置问题的模型构建都是基于模型参数等完全确定且只考虑保险公司本身的利益的角度。近年来,随着随机控制理论的发展及学科间交流的增多,对保险公司资产配置的研究进入了多元化发展的阶段。本文结合行为金融学等理论的思想,以随机控制理论为技术手段,针对模型不确定性建立鲁棒优化体系,同时考虑保险公司和再保险公司双方的收益,研究投资和再保险等资产配置问题,这对丰富保险风险模型理论体系具有重要的实际意义和理论价值。考虑模型不确定性这一因素对模型构建、目标求解等方面的影响,结合行为金融学的的思想,通过将保险公司和再保险公司视为“模糊厌恶”偏向的决策者,量化模型不确定性这一影响因素,将普通投资-再保险问题转化为鲁棒最优投资-再保险问题进行研究。同时,考虑到保险公司开展的再保险业务涉及到再保险公司的利益,故本研究立足于解决保险公司和再保险公司的联合最优投资-再保险问题,在风险资产的价格过程发生不同变化的情形下对问题进行系统研究。首先构建Black-Scholes市场中再保险双方的资产盈余模型,保险公司为转移风险采取比例再保险的再保险策略,同时保险公司和再保险公司均可投资至金融市场的风险资产,并且保险集团的决策者是模糊厌恶的投资者,以最大化加权盈余过程终端财富的最小期望效用为优化目标,寻求鲁棒最优的投资-再保险策略。利用随机控制理论,分别推导保险公司和再保险公司的鲁棒最优投资-再保险策略,并通过数值例子对最优策略进行敏感性分析,深化研究结论。考虑到风险资产收益并非是常数,而是具有时变性和“波动率聚集”等特性,在风险资产由Black-Scholes模型刻画的再保险双方联合最优资产分配模型的基础上进行深入研究,当风险资产的价格过程服从具有随机波动率的Heston模型时,构建了保险公司和再保险公司的投资-再保险模型,确立保险公司和再保险公司联合资产配置的鲁棒优化目标,通过运用动态规划原理,得到了最优的投资-再保险策略,并对此最优策略进行深入研究、分析。一般而言,对于再保险双方联合资产配置问题的优化目标的构建是通过对两者财富过程进行加权和处理得到一个新的财富过程,进而最大化这个新的财富过程的终端效用来实现的。本研究还试图由一个全新的角度来研究再保险双方联合的投资-再保险问题,即研究使得保险公司和再保险公司终端财富在指数乘积效用函数下最大化的资产配置策略,使得研究角度更加多样化。由于均值-方差投资组合选择问题和期望效用的框架下的优化问题,都会产生时间不一致性随机控制问题。本研究通过引入博弈论的思想定义均衡策略及均衡值函数的概念,在保险公司和再保险公司均投资至金融市场的条件下,确立保险公司和再保险公司联合资产配置的鲁棒优化目标,建立对于保险公司和再保险公司财富过程的扩展的HJB方程,求解扩展HJB方程的解并验证它确实为最优策略,最后再通过数值例子使得结论更形象、丰富。
[Abstract]:The problem of asset allocation of insurance companies has always been a hot topic in the field of actuarial research. Its main configuration methods include reinsurance, investment, dividend and so on. How to choose reasonable investment and reinsurance strategy to share risk, stabilize operation and improve the enterprise strength of insurance companies has been the important research content of insurance actuaries.20 70 century. Since the years, the model construction of the insurance company's asset allocation problem is based on the model parameters and the benefit of the insurance company itself. In recent years, with the development of the stochastic control theory and the increase of interdisciplinary exchange, the research on the asset allocation of insurance companies has entered a diversified development stage. According to the theory of behavioral finance and so on, the theory of random control is used as the technical means to establish a robust optimization system for model uncertainty, and to consider the benefits of both insurance companies and reinsurance companies, and to study the asset allocation problems such as investment and reinsurance, which is of great practical significance to the theory of enriching the insurance risk model. Considering the influence of model uncertainty to model construction, objective solution and so on, combined with the thought of behavioral finance, by taking insurance companies and reinsurance companies as "fuzzy disgust" decision-makers, quantifying the uncertainty of the model, transforming the common investment reinsurance problem into Lu. At the same time, considering that the reinsurance business carried out by the insurance company involves the benefits of the reinsurance company, this study is based on solving the joint optimal investment reinsurance problem of the insurance company and the reinsurance company and the problem in the case of different changes in the price process of the risk assets. First, the asset surplus model of the reinsurance parties in the Black-Scholes market is built, and the insurance company adopts the reinsurance strategy of proportional reinsurance for the transfer risk. At the same time, the insurance companies and the reinsurance companies can invest in the risk assets of the financial market, and the decision-makers of the insurance group are the fuzzy aversion investors. The minimum expected utility of the terminal wealth of the weighted surplus process is the optimization goal and the optimal investment reinsurance strategy is sought. Using the stochastic control theory, the robust optimal investment reinsurance strategy of insurance companies and reinsurance companies is derived, and the optimal strategy is analyzed by numerical examples and the conclusion is deepened. Considering that the income of risk assets is not a constant, it has the characteristics of time-varying and "volatility aggregation". On the basis of the joint optimal asset allocation model of the reinsurance parties, which is characterized by the Black-Scholes model, the risk asset is studied. When the price of the risk asset over Cheng Fucong has the Heston model of random volatility, it is constructed. The investment and reinsurance model of insurance companies and reinsurance companies is built, and the robust optimization goal of the joint asset allocation of insurance companies and reinsurance companies is established. By using the dynamic programming principle, the optimal investment reinsurance strategy is obtained, and the optimal strategy is deeply studied and analyzed. Generally speaking, the two parties are combined with the reinsurance. The optimization goal of the asset allocation problem is to build a new wealth process by weighting and dealing with the two wealth processes, and thus maximizing the terminal efficiency of the new wealth process. This study also tries to study the joint reinsurance problem of the two parties from a new perspective, that is, the study of the reinsurance problem. The asset allocation strategy, which maximizes the terminal wealth of insurance companies and reinsurance companies under the exponential product utility function, makes the research perspective more diverse. Due to the optimization problem under the framework of the mean variance portfolio selection problem and the expected utility, the stochastic control problem of time inconsistency will be generated. The concept of equilibrium strategy and equilibrium value function is defined by the theory of game theory. Under the conditions of both insurance companies and reinsurance companies to invest in the financial market, the robust optimization goal of the joint asset allocation of insurance companies and reinsurance companies is established, and the HJB equation for the expansion of the wealth process of insurance companies and reinsurance companies is established, and the extended H is solved. The solution of the JB equation is proved to be the optimal strategy. Finally, numerical examples are used to make the conclusion more vivid and rich.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F842.69
，
本文编号：2123232
[Abstract]:The problem of asset allocation of insurance companies has always been a hot topic in the field of actuarial research. Its main configuration methods include reinsurance, investment, dividend and so on. How to choose reasonable investment and reinsurance strategy to share risk, stabilize operation and improve the enterprise strength of insurance companies has been the important research content of insurance actuaries.20 70 century. Since the years, the model construction of the insurance company's asset allocation problem is based on the model parameters and the benefit of the insurance company itself. In recent years, with the development of the stochastic control theory and the increase of interdisciplinary exchange, the research on the asset allocation of insurance companies has entered a diversified development stage. According to the theory of behavioral finance and so on, the theory of random control is used as the technical means to establish a robust optimization system for model uncertainty, and to consider the benefits of both insurance companies and reinsurance companies, and to study the asset allocation problems such as investment and reinsurance, which is of great practical significance to the theory of enriching the insurance risk model. Considering the influence of model uncertainty to model construction, objective solution and so on, combined with the thought of behavioral finance, by taking insurance companies and reinsurance companies as "fuzzy disgust" decision-makers, quantifying the uncertainty of the model, transforming the common investment reinsurance problem into Lu. At the same time, considering that the reinsurance business carried out by the insurance company involves the benefits of the reinsurance company, this study is based on solving the joint optimal investment reinsurance problem of the insurance company and the reinsurance company and the problem in the case of different changes in the price process of the risk assets. First, the asset surplus model of the reinsurance parties in the Black-Scholes market is built, and the insurance company adopts the reinsurance strategy of proportional reinsurance for the transfer risk. At the same time, the insurance companies and the reinsurance companies can invest in the risk assets of the financial market, and the decision-makers of the insurance group are the fuzzy aversion investors. The minimum expected utility of the terminal wealth of the weighted surplus process is the optimization goal and the optimal investment reinsurance strategy is sought. Using the stochastic control theory, the robust optimal investment reinsurance strategy of insurance companies and reinsurance companies is derived, and the optimal strategy is analyzed by numerical examples and the conclusion is deepened. Considering that the income of risk assets is not a constant, it has the characteristics of time-varying and "volatility aggregation". On the basis of the joint optimal asset allocation model of the reinsurance parties, which is characterized by the Black-Scholes model, the risk asset is studied. When the price of the risk asset over Cheng Fucong has the Heston model of random volatility, it is constructed. The investment and reinsurance model of insurance companies and reinsurance companies is built, and the robust optimization goal of the joint asset allocation of insurance companies and reinsurance companies is established. By using the dynamic programming principle, the optimal investment reinsurance strategy is obtained, and the optimal strategy is deeply studied and analyzed. Generally speaking, the two parties are combined with the reinsurance. The optimization goal of the asset allocation problem is to build a new wealth process by weighting and dealing with the two wealth processes, and thus maximizing the terminal efficiency of the new wealth process. This study also tries to study the joint reinsurance problem of the two parties from a new perspective, that is, the study of the reinsurance problem. The asset allocation strategy, which maximizes the terminal wealth of insurance companies and reinsurance companies under the exponential product utility function, makes the research perspective more diverse. Due to the optimization problem under the framework of the mean variance portfolio selection problem and the expected utility, the stochastic control problem of time inconsistency will be generated. The concept of equilibrium strategy and equilibrium value function is defined by the theory of game theory. Under the conditions of both insurance companies and reinsurance companies to invest in the financial market, the robust optimization goal of the joint asset allocation of insurance companies and reinsurance companies is established, and the HJB equation for the expansion of the wealth process of insurance companies and reinsurance companies is established, and the extended H is solved. The solution of the JB equation is proved to be the optimal strategy. Finally, numerical examples are used to make the conclusion more vivid and rich.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F842.69
，
本文编号：2123232
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