均值—方差再保险—投资策略选择问题

发布时间：2018-05-29 13:30

本文选题：均值-方差 + 时间一致性　；参考：《中南大学》2013年硕士论文

【摘要】：摘要：我们考虑了对于保险者的一个最优的时间一致的再保险-投资策略选择问题,保险者的盈余过程是由一个线性扩散控制的。在我们的模型当中,保险者在一个简单的金融市场当中,通过比例再保险和投资盈余来产生保险索赔来转移部分风险,这里我们所说的金融市场是由一个无风险资产和一个风险资产构成的。在本文当中,我们首先考虑风险资产的动态由CEV模型来控制的,这个CEV模型包括了条件异方差还有资产价格在波动率上的反馈影响。保险者的目标就是选择一个最优的时间一致的再保险-投资策略当最小化终端盈余方差时来最大化终端盈余的期望。我们使用Hamilton-Jacobi-Bellman (H-J-B)动态规划方法来解决这个问题。我们得到了最优的再保险-投资策略和相应值函数的显式形式解。而且,我们给出了一些数值例子来说明当一些模型参数改变的时候我们的最优再保险-投资策略是如何改变的。最后,我们研究了风险资产的动态由O-U过程控制的情形,我们同样得到了一个最优的时间一致的均值-方差投资策略和相应值函数的显式形式解。
[Abstract]:Absrtact: we consider an optimal time consistent reinsurance-investment strategy selection problem for the insurer whose surplus process is controlled by a linear diffusion. In our model, in a simple financial market, insurers generate insurance claims through proportional reinsurance and investment surpluses to transfer part of the risk. The financial market here is composed of a risk-free asset and a risk-free asset. In this paper we first consider that the dynamic of risky assets is controlled by CEV model which includes conditional heteroscedasticity and feedback of asset price volatility. The goal of the insurer is to select an optimal time consistent reinsurance-investment strategy to maximize the end earnings expectation when minimizing the end earnings variance. We use Hamilton-Jacobi-Bellman-J-(-) dynamic programming to solve this problem. We obtain the explicit solution of the optimal reinsurance-investment strategy and the corresponding value function. Furthermore, we give some numerical examples to illustrate how our optimal reinsurance-investment strategy changes when some model parameters change. Finally, we study the case that the dynamic of risky assets is controlled by O-U process. We also obtain an optimal time-consistent mean-variance investment strategy and explicit solution of the corresponding value function.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.69;F224

【共引文献】