复杂金融模型下的保险公司最优再保险和投资策略研究

发布时间：2018-05-10 20:37

本文选题：再保险 + 投资　；参考：《上海交通大学》2015年博士论文

【摘要】：保险公司通过购买再保险将索赔损失部分转移给其它保险公司,从而达到分散风险、稳定经营的目的。同时,为了增强偿付能力,增加利润来源,投资业务在保险公司中也扮演着越来越重要的角色。因此,保险精算中的最优再保险和投资问题成为最近热门的研究课题之一。过去几十年来,随机控制理论和方法越来越广泛地应用于投资组合优化和再保险优化的研究中。本文假定保险公司索赔服从复合泊松过程或带有漂移的布朗运动,利用随机过程理论和随机控制方法,研究保险公司在几类复杂金融模型下的最优再保险和投资策略。主要内容包括:首先,考虑保险公司拥有两类性质不同的保险业务。一类业务的索赔风险比较集中,采用期望值保费原理收取保费和支出再保费,通过购买超额损失再保险分散风险;而另一类业务的索赔风险波动较大,采用方差保费原理,购买比例再保险。分别在调节系数最大化准则和期望效用准则下,求解最优比例再保险和最优超额损失再保险策略。结果显示,调节系数和风险厌恶系数具有相似的作用。第二,利用常弹性方差(CEV)过程描述风险资产的价格,以刻画随机方差。保险公司除了购买比例再保险或超额再保险外,还将部分盈余投资于CEV风险资产。其目标是期末财富期望效用最大化,利用随机控制理论得到最优策略和值函数。结果显示,投资策略除了包括经典的Merton投资策略外,还含有根据弹性系数、时间和风险资产价格所做的调整项。第三,利用指数均值回复过程模拟风险资产价格,以描述其收益的均值回复现象。保险公司将部分盈余投资于指数回复金融市场,同时购买比例和超额损失组合再保险。在效用最大化准则下分析了保险公司的最优投资策略和再保险策略。结果表明保险公司总是选择一个纯的超额损失再保险策略。同时投资策略也是在Merton投资策略基础上加上根据回复速率、时间和资产价格所做的调整项。第四,用Lévy过程刻画金融风险资产的价格,以捕获价格的跳。考虑更为一般的均值-方差准则,导致财富路径相依的优化问题。利用随机控制理论和拉格朗日乘子法,得到最优投资和再保险策略,并在经典均值-方差模型中分析了方差最小边界和有效前沿。结果显示投资策略不仅与风险溢价有关,还与当前财富水平成正比。而再保险策略与保单的损失强度成正比。本文的贡献和创新主要体现在下列几个方面。(1)对风险特性不同的保险业务采用不同的保费原理和再保险形式。在扩散近似模型下,得到了保险公司的调节系数和最小化破产概率下的再保险策略,以及期望效用最大化下的再保险策略。并分析了调节系数和风险偏好系数的作用。(2)采用常弹性方差过程描述资产价格的随机方差。当保险盈余过程采用复合泊松过程时,使用方差保费原理,并附加净利润条件的限制,得到了约束条件下的最优比例再保险策略和投资策略。当采用扩散近似盈余过程时,使用期望值保费原理,得到了最优超额损失再保险策略和投资策略,并证明了该模型下超额损失再保险总是优于比例再保险。(3)在期望效用最大化准则下得到了均值回复模型中的最优投资策略和比例-超额损失组合再保险策略,并用不同于其它文献的方法证明了,一定条件下,超额损失再保险也总是优于比例-超额损失组合再保险。(4)采用Lévy过程描述金融资产价格的跳,在财富路径相依的广义均值-方差准则下得到了最优比例再保险和投资策略,并得到了在经典均值-方差模型下的方差最小边界和有效前沿。
[Abstract]:The insurance company transfers the claim loss part to other insurance companies through the purchase of reinsurance, thus achieving the goal of dispersing the risk and stabilizing the operation. At the same time, in order to enhance the solvency and increase the profit source, the investment business is also playing an increasingly important role in the insurance company. Therefore, the optimal reinsurance and investment in the actuarial actuarial question is asked. The problem has become one of the most popular research topics. In the past few decades, the theory and methods of random control have been used more and more widely in the study of portfolio optimization and reinsurance optimization. This paper assumes that the insurance company's claim obeys the compound Poisson process or the Brown movement with drift, and uses the stochastic process theory and the random control method. The main contents of the insurance companies under several types of complex financial models are as follows: first, the insurance companies have two kinds of insurance business with different types of insurance. The claim risk of a class of business is concentrated, the premium and the reinsurance premium are collected by the expected premium principle, and the excess loss reinsurance is purchased. While the risk of the other kind of business is fluctuant, the variance premium principle and the purchase ratio reinsurance are adopted. The optimal ratio reinsurance and the optimal excess loss reinsurance strategy are solved under the maximization of the regulation coefficient and the expected utility criterion respectively. The results show that the joint coefficient and the risk aversion coefficient have a similar effect. Two, the CEV process is used to describe the price of risk assets to describe the random variance. In addition to the purchase of proportional reinsurance or excess reinsurance, the insurance company also invested part of the surplus in the CEV risk asset. The goal is to maximize the expected utility of the end of the wealth and obtain the optimal strategy and value function by using the stochastic control theory. It shows that, in addition to the classic Merton investment strategy, the investment strategy also contains adjustment items based on the elastic coefficient, time and risk asset prices. Third, the mean return process is used to simulate the value of the risk asset price to describe the mean return of its earnings. At the same time, the purchase ratio and excess loss combination reinsurance. The optimal investment strategy and reinsurance strategy are analyzed under the maximization of utility. The result shows that the insurance company always chooses a pure excess loss reinsurance strategy. At the same time, the investment strategy is based on the response rate and time based on the Merton investment strategy. The adjustment item made by the asset price. Fourth, the L e vy process is used to describe the price of the financial risk assets to capture the price jump. Considering the more general mean variance criterion, the optimal problem of the dependence of the wealth path is caused. The optimal investment and reinsurance strategy is obtained by using the stochastic control theory and the Lagrange multiplier method, and the classic mean value is obtained. In the variance model, the minimum variance boundary and the effective frontier are analyzed. The results show that the investment strategy is not only related to the risk premium, but also directly proportional to the current wealth level. The reinsurance strategy is proportional to the loss intensity of the policy. The contribution and innovation of this paper are mainly reflected in the following aspects. (1) the insurance business with different risk characteristics is adopted. Different premium principle and reinsurance form. Under the diffusion approximation model, the adjustment coefficient of insurance companies and the reinsurance strategy under the minimum ruin probability and the reinsurance strategy under the maximum expected utility are obtained. The effect of the adjustment coefficient and the risk preference coefficient is analyzed. (2) the asset price is described by the constant elastic variance process. When the insurance surplus process adopts the compound Poisson process, the optimal proportion reinsurance strategy and investment strategy under the constraint conditions are obtained by using the principle of variance premium and the restriction of net profit conditions. When the diffusion approximate surplus process is adopted, the optimal excess loss reinsurance policy is obtained by using the expected value premium principle. It is proved that excess loss reinsurance under this model is always better than proportional reinsurance. (3) under the maximization of expected utility, the optimal investment strategy and the proportional excess loss combination reinsurance strategy are obtained in the mean return model, and the excess loss is proved under certain conditions. The reinsurance is always better than the proportion super loss combination reinsurance. (4) the L e vy process is used to describe the price jump of financial assets, and the optimal proportional reinsurance and investment strategy is obtained under the generalized mean variance criterion of the wealth path dependence, and the minimum variance boundary and effective frontier under the classical mean variance model are obtained.

【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：F224;F842.3

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