带红利与交易费用的最优投资问题研究

发布时间：2018-07-24 20:10

【摘要】：目前,大部分研究只考虑了保险公司的投资问题而忽略了再保险公司的管理.但是再保险公司也会面临破产,也需要投资它的资产到金融市场去管理它的财富.所以,本文主要研究了在保险公司能够购买比例再保险的条件下,保险公司和再保险公司的最优投资问题.并且我们得到了关于保险公司的终端财富期望指数效用最大化和再保险公司的终端财富期望指数效用最大化以及破产概率最小化的相关结论.本文主要工作如下：第一章,简单概括了保险公司和再保险公司的研究背景及其最新研究动态.接着介绍了本文的主要内容及其结论.第二章,主要介绍了几种索赔过程和盈余过程以及本文将要用到的风险市场投资的价格过程.第三章,首先,运用布朗运动与漂移项刻画了保险公司的索赔过程；其次,我们认为保险公司可以购买比例再保险来降低潜在的风险,因此得到了它的盈余过程；然后,假定保险公司能够将它的盈余以无风险资产和风险资产的形式投资到金融市场,从而得到了其财富过程,其中保险公司的风险资产是由一个几何布朗运动来刻画的；最后,通过运用随机控制理论解决值函数所满足的HJB方程,得到了保险公司的最优比例再保险和终端财富期望指数效用最大化下的最优投资策略.第四章,在第三章保险公司得到的最优比例再保险的条件下,我们分别得到了再保险公司在终端财富期望指数效用最大化和破产概率最小化条件下的最优投资策略.然后说明了再保险公司在期望指数效用最大化和破产概率最小化这两种情况下最优投资策略的等价性.第五章,介绍了再保险公司可以将它的盈余以无风险资产和风险资产的形式投资于金融市场,其中风险资产是由经典的CEV模型来刻画的.通过解决相应的HJB方程以及效用函数中所使用的幂变换,得到了最优投资策略.
[Abstract]:At present, most studies only consider the investment of insurance companies and ignore the management of reinsurance companies. But the reinsurer also faces bankruptcy and needs to invest its assets in financial markets to manage its wealth. Therefore, this paper mainly studies the optimal investment of insurance companies and reinsurance companies under the condition that insurance companies can buy proportional reinsurance. Furthermore, we obtain some conclusions about the utility maximization of the end-wealth expectation index of the insurance company, the maximum utility of the end-wealth expectation index of the reinsurance company and the minimization of the ruin probability. The main work of this paper is as follows: the first chapter briefly summarizes the research background and the latest research trends of insurance companies and reinsurance companies. Then the main contents and conclusions of this paper are introduced. The second chapter mainly introduces several kinds of claim process and earnings process as well as the price process of risk market investment which will be used in this paper. In chapter 3, firstly, we use Brownian motion and drift term to describe the claim process of insurance company; secondly, we think that insurance company can buy proportional reinsurance to reduce the potential risk, so we get its surplus process. Assuming that the insurance company can invest its surplus in the financial market in the form of risk-free assets and riskless assets, the process of its wealth is obtained, in which the risky assets of the insurance company are characterized by a geometric Brownian motion; finally, By using stochastic control theory to solve the HJB equation satisfied by the value function, the optimal investment strategy of insurance companies under optimal proportional reinsurance and terminal wealth expectation index utility maximization is obtained. In chapter 4, under the condition of optimal proportional reinsurance obtained by insurance companies in chapter 3, we obtain the optimal investment strategies of reinsurance companies under the conditions of maximum utility of terminal wealth expectation index and minimization of ruin probability respectively. Then we prove the equivalence of optimal investment strategies for reinsurance companies in the case of optimal exponential utility maximization and ruin probability minimization. Chapter five introduces that the reinsurance company can invest its surplus in the financial market in the form of risk-free assets and riskless assets, in which the risky assets are described by the classical CEV model. The optimal investment strategy is obtained by solving the corresponding HJB equation and the power transformation used in the utility function.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F842.3

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