随机利率和随机波动率下最优投资和再保险问题研究

发布时间：2018-01-15 02:25

本文关键词：随机利率和随机波动率下最优投资和再保险问题研究　出处：《天津工业大学》2016年硕士论文　论文类型：学位论文

【摘要】：保险公司如何有效进行投资和购买再保险实现公司价值最大化、风险最小化已成为一个重要研究课题。为了寻找具有实际价值的最优策略,本文分别从两个方面研究了随机利率和随机波动率环境下的最优投资和再保险策略：一方面研究使得终端财富幂效用函数最大化的情况；另一方面研究在终端财富为定值时,使得终值方差最小,即风险最小的情况。主要工作如下：1.随机环境下基于幂效用目标的最优化问题。保险公司通过购买比例再保险来分散部分风险的同时,将资产投资于无风险资产和风险资产,其中无风险资产的利率采用随机Vasicek利率模型描述及风险资产波动率采用Heston随机波动率模型描述。目标是选择最优的投资和再保险策略使得终端财富的幂效用函数最大,并求出相应的值函数。主要利用随机动态规划方法求得最优问题的HJB方程,最终求得最优再保险比例和投资策略,并通过算例进行分析。2.随机环境下基于均值-方差准则目标的最优化问题。保险公司同样购买比例再保险,投资于无风险资产和风险资产,目标是在保险公司终端财富为定值时,选择最优策略使终值方差最小,即风险最小,并且求得最小方差。针对此问题,主要利用Lagrange对偶定理,将均值-方差问题转化为不带约束的最优控制问题。进一步,利用动态规划原理的方法求解,通过转化求得原问题的最优投资和再保险策略。最后,给出文章的结论,并展望今后值得深入研究的方向。
[Abstract]:The insurance company how to effectively carry out investment and maximize the value of the company to purchase reinsurance, risk minimization has become an important research topic. In order to find the optimal strategy has practical value, this paper from the two aspects of the stochastic interest rate and stochastic volatility optimal investment and reinsurance strategy under study: on the one hand so that the terminal wealth power maximize the utility function of the situation; on the other hand in the terminal wealth as the fixed value, the value of the minimum variance, i.e. the minimum risk. The main work is as follows: 1. the stochastic optimization problem under the environment of power utility based on the target. The insurance company to disperse risk by purchasing proportional reinsurance and investment in free will risk assets and risk assets, the risk free interest rate of assets by the random Vasicek interest rate model to describe the risk and volatility of assets by He Ston stochastic volatility model is described. The target is the power utility function and the optimal reinsurance strategy investment choice makes the terminal wealth maximum, and calculated the value of the corresponding function. HJB equation to obtain the optimal problem by using stochastic dynamic programming method, finally obtain the optimal reinsurance ratio and investment strategy, and through the example analysis of.2. random environment the optimization problem under the mean variance criterion based on the target. The insurance company will purchase proportional reinsurance, invest in a riskless asset and risky asset, the target is in the insurance company terminal wealth as the fixed value, the value of the minimum variance optimal strategy choice, namely the minimum risk, and obtain the minimum variance. To solve this problem, the main use of Lagrange dual the theorem, the mean variance problem into unconstrained optimal control problems. Further, by using the method of solving the dynamic programming principle, through the transformation The optimal investment and reinsurance strategy of the original problem are obtained. Finally, the conclusion of the article is given and the direction for further study is expected.

【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F840;O224

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