最优投资再保险策略的相关研究

发布时间：2018-04-27 13:12

本文选题：投资再保险策略 + 效用函数　；参考：《华东师范大学》2017年博士论文

【摘要】：保险公司作为市场经济中不可或缺的一环,通过向个人和集体售卖保单而获取保费并为其提供金融保护。对于所获得的利润保险人可以将其投资到金融市场之中,通过购买股票债券等形式获取更大的收益。但由于资金与规模的限制,保险公司有时候还需要将自己承担的一部分保险风险和收益转让给再保险公司,即支付一定量的再保费而换取再保险公司去承担一部分保险风险损失。在这样的经营过程中,一个自生的问题是如何选择投资股票和债券的额度以及购买再保险的数量和种类。我们将这样一类问题归结为最优投资再保险问题。本文对不同模型下的最优投资再保险策略的相关问题展开若干研究。主要工作如下:(1)针对较广义的两段式效用函数模型,我们在第二章讨论了相关的最优投资再保险策略和值函数的形式。基于鞅理论和凸优化的方法,我们将原本动态的最优化问题转变成求解一个静态最优化问题的解。通过得到的终端变量的形式求解相关的条件期望,比较后获得最优投资再保险策略的形式。此外我们还给出了所求形式下常见的几个效用函数的最优策略。(2)对于财险型的保险公司,方差保费原理有着更加广泛的应用和实际意义。第三章中我们将基于方差保费原理之下考虑保险人的最优投资再保险问题。为了能够更好的描述市场的变化我们用一个连续时间的马氏链去描述模型参数的变化也即经典的Regime-Switching模型,并考虑了两种不同风险模型下的最优策略。此外我们还对保险人能够投资到证券市场的金额以及所能购买的再保险份额进行了限制,使得我们的模型更具有实际意义。(3)在以往的工作中,最优再保险问题大都是基于保险人的角度去考虑的。文献中很少将最优再保险问题从再保险人的角度或者双方的角度去考虑。然而作为一个由保险人和再保险人双方共同制定的再保险合约,仅考虑保险人的角度从某种意义上来说是不完整的。换句话说,一个再保险合约仅考虑任何一方的利益都可能为另一方所不接受。第四章中我们将兼顾保险人和再保险人双方的利益,建立并研究保险人与再保险人之间的Stackelberg博弈问题。再保险人由于其雄厚的资本和较强的抗风险能力处于博弈中领导者的地位,而保险人则只能作为追随者。我们将在最大化期望指数效用这样一个目标函数下考虑博弈问题并通过求解两个相联系的HJB方程得到相应的最优策略。(4)延续上一章的讨论,我们将在金融理论中另外一个被广泛应用的模型:均值-方差模型下研究Stackelberg博弈中保险人和再保险人的最优均衡策略。由于模型的目标函数无法写成一个关于终端变量或财富函数的期望,贝尔曼最优化原理并不成立,也使得我们在解决这类问题时无法应用一般的动态规划准则去推导HJB方程。我们会应用Bjork and Murgoci[16]中的理论去解决这样的时间不一致问题并通过两个广义HJB方程的求解而得到相关的均衡策略。在这一章中我们将分别考虑比例再保险和超额损失再保险两种再保险形式。本文的结论与成果丰富了最优投资再保险问题的研究,有助于保险人和再保险人分析和选择相关的投资再保险策略。
[Abstract]:As an integral part of the market economy, insurance companies obtain premium and provide financial protection by selling insurance policies to individuals and collectives. For the profit insurer, the insurer can invest it in the financial market and obtain greater returns by buying stock bonds. A risk company sometimes needs to transfer some of its insurance risks and benefits to the reinsurance company, that is, to pay a certain amount of reinsurance for the reinsurance company to take on a part of the insurance risk loss. In such a process, a self born question is how to choose the amount of the investment stock and bond and the purchase. The number and type of reinsurance. We attribute such a kind of problem to the optimal investment reinsurance problem. This paper studies the related problems of the optimal investment reinsurance strategy under different models. The main work is as follows: (1) for the more generalized two segment utility function model, we discuss the related optimal investment in the second chapter. Based on the martingale theory and the method of convex optimization, we transform the original dynamic optimization problem into a solution to a static optimization problem. We obtain the related conditional expectation by the form of the terminal variables obtained, and then obtain the optimal investment reinsurance strategy after comparison. In addition, we give the results. The optimal strategies for several common utility functions are found in the form. (2) for the insurance companies of financial insurance, the principle of variance premiums has more extensive application and practical significance. In the third chapter, we will consider the optimal investment reinsurance problem of the insurer under the principle of variance premium in order to better describe the changes in the market. A continuous time Markov chain is used to describe the variation of the model parameters, that is, the classical Regime-Switching model, and the optimal strategy under two different risk models is considered. In addition, we also restrict the amount of the insurer to invest in the stock market and the amount of the reinsurance that can be purchased, making our model more useful. There are practical significance. (3) in the past, most of the best reinsurance problems are considered based on the perspective of the insurer. In the literature, the best reinsurance problem is considered from the angle of reinsurance or the angle of both parties. However, as a reinsurance contract jointly formulated by both the insurer and the reinsurance person, only the insurance is considered. A person's angle is incomplete in a sense. In other words, a reinsurance contract only considering the interests of any party may not be accepted by the other party. In the fourth chapter, we will take into account the interests of both the insurer and the reinsurance party, and establish and study the Stackelberg game between the insurer and the reinsurance person. People are in the position of leaders in the game because of their strong capital and strong anti risk ability, and the insurer can only be the followers. We will consider the game problem under the objective function of maximizing the expectation index utility and obtain the corresponding optimal strategy by solving the two HJB equation. (4) continuation of the last chapter We will study the optimal equilibrium strategy of the insurer and reinsurance in the Stackelberg game under the mean variance model in the financial theory, which is widely used in the financial theory. Because the objective function of the model can not be written as a expectation of the terminal variable or the wealth function, the Behrman optimization principle is not set up. We can not apply the general dynamic programming criterion to deduce the HJB equation when solving these problems. We will apply the theory of Bjork and Murgoci[16] to solve such a time inconsistency problem and get the related equilibrium strategy by solving two generalized HJB equations. In this chapter, we will consider the proportional reinsurance respectively. The conclusions and results of this paper enrich the research on the problem of optimal investment reinsurance, which will help the insurers and reinsurers to analyze and select related investment reinsurance strategies. The results and results of this paper are two reinsurance forms.

【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F224;F842.3

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