再保險雙方的聯(lián)合魯棒最優(yōu)投資—再保險策略研究
發(fā)布時間：2018-07-15 07:09
【摘要】：保險公司的資產(chǎn)配置問題一直是保險精算領(lǐng)域的研究熱點,其主要的配置方式包括再保險、投資、分紅等。如何選擇合理的投資、再保險策略,以分攤風(fēng)險、穩(wěn)定經(jīng)營、提升保險公司的企業(yè)實力一直是保險精算學(xué)者的重要研究內(nèi)容。20世紀70年代以來,對保險公司資產(chǎn)配置問題的模型構(gòu)建都是基于模型參數(shù)等完全確定且只考慮保險公司本身的利益的角度。近年來,隨著隨機控制理論的發(fā)展及學(xué)科間交流的增多,對保險公司資產(chǎn)配置的研究進入了多元化發(fā)展的階段。本文結(jié)合行為金融學(xué)等理論的思想,以隨機控制理論為技術(shù)手段,針對模型不確定性建立魯棒優(yōu)化體系,同時考慮保險公司和再保險公司雙方的收益,研究投資和再保險等資產(chǎn)配置問題,這對豐富保險風(fēng)險模型理論體系具有重要的實際意義和理論價值。考慮模型不確定性這一因素對模型構(gòu)建、目標(biāo)求解等方面的影響,結(jié)合行為金融學(xué)的的思想,通過將保險公司和再保險公司視為“模糊厭惡”偏向的決策者,量化模型不確定性這一影響因素,將普通投資-再保險問題轉(zhuǎn)化為魯棒最優(yōu)投資-再保險問題進行研究。同時,考慮到保險公司開展的再保險業(yè)務(wù)涉及到再保險公司的利益,故本研究立足于解決保險公司和再保險公司的聯(lián)合最優(yōu)投資-再保險問題,在風(fēng)險資產(chǎn)的價格過程發(fā)生不同變化的情形下對問題進行系統(tǒng)研究。首先構(gòu)建Black-Scholes市場中再保險雙方的資產(chǎn)盈余模型,保險公司為轉(zhuǎn)移風(fēng)險采取比例再保險的再保險策略,同時保險公司和再保險公司均可投資至金融市場的風(fēng)險資產(chǎn),并且保險集團的決策者是模糊厭惡的投資者,以最大化加權(quán)盈余過程終端財富的最小期望效用為優(yōu)化目標(biāo),尋求魯棒最優(yōu)的投資-再保險策略。利用隨機控制理論,分別推導(dǎo)保險公司和再保險公司的魯棒最優(yōu)投資-再保險策略,并通過數(shù)值例子對最優(yōu)策略進行敏感性分析,深化研究結(jié)論�？紤]到風(fēng)險資產(chǎn)收益并非是常數(shù),而是具有時變性和“波動率聚集”等特性,在風(fēng)險資產(chǎn)由Black-Scholes模型刻畫的再保險雙方聯(lián)合最優(yōu)資產(chǎn)分配模型的基礎(chǔ)上進行深入研究,當(dāng)風(fēng)險資產(chǎn)的價格過程服從具有隨機波動率的Heston模型時,構(gòu)建了保險公司和再保險公司的投資-再保險模型,確立保險公司和再保險公司聯(lián)合資產(chǎn)配置的魯棒優(yōu)化目標(biāo),通過運用動態(tài)規(guī)劃原理,得到了最優(yōu)的投資-再保險策略,并對此最優(yōu)策略進行深入研究、分析。一般而言,對于再保險雙方聯(lián)合資產(chǎn)配置問題的優(yōu)化目標(biāo)的構(gòu)建是通過對兩者財富過程進行加權(quán)和處理得到一個新的財富過程,進而最大化這個新的財富過程的終端效用來實現(xiàn)的。本研究還試圖由一個全新的角度來研究再保險雙方聯(lián)合的投資-再保險問題,即研究使得保險公司和再保險公司終端財富在指數(shù)乘積效用函數(shù)下最大化的資產(chǎn)配置策略,使得研究角度更加多樣化。由于均值-方差投資組合選擇問題和期望效用的框架下的優(yōu)化問題,都會產(chǎn)生時間不一致性隨機控制問題。本研究通過引入博弈論的思想定義均衡策略及均衡值函數(shù)的概念,在保險公司和再保險公司均投資至金融市場的條件下,確立保險公司和再保險公司聯(lián)合資產(chǎn)配置的魯棒優(yōu)化目標(biāo),建立對于保險公司和再保險公司財富過程的擴展的HJB方程,求解擴展HJB方程的解并驗證它確實為最優(yōu)策略,最后再通過數(shù)值例子使得結(jié)論更形象、豐富。
[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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：F224;F842.69
，
本文編號：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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：F224;F842.69
，
本文編號：2123232
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