常弹性方差模型下的最优再保险和投资研究

发布时间：2018-03-28 19:10

本文选题：随机最优控制　切入点：再保险　出处：《暨南大学》2013年硕士论文

【摘要】：随着保险行业的蓬勃发展，保险规模逐渐扩大，保险公司面临的风险也不断增大。为了分散风险，，稳定经营，保险公司需要采取再保险的措施来将自身部分风险转移出去。而在减少风险同时必然伴随着保费的分摊，对保险公司而言意味着可盈利的资本减少，所以保险公司需要在再保险的收益与风险两者关系中达到平衡。同时保险公司为追求盈利可以将积累的保费投资于金融市场获取预期收益。投资带来风险，将必然面临投资收益与风险的抉择问题。因此，探索最优再保险和投资策略对保险公司的发展而言至关重要。本文主要运用随机最优控制理论，通过建立动态规划模型来解决最优再保险和投资问题。首先在扩散风险模型中引入再保险。当保险公司将盈余投资到常数弹性变差（CEV）模型描述的风险资产和无风险资产时，应用动态规划原理以期望效用最大化为目标取得值函数满足的HJB方程。然后利用Legendre变化-对偶方法在不同效用函数准则下，得到最优再保险和投资策略。最后结合数值图像分析各个相关参数与最优再保险投资策略之间的联系。
[Abstract]:With the booming development of the insurance industry, the scale of insurance is gradually expanding, and the risks faced by insurance companies are also increasing. Insurance companies need to take reinsurance measures to transfer part of their own risk. And reducing risk must be accompanied by premium allocation, which means less profitable capital for insurance companies. So insurance companies need to strike a balance between reinsurance returns and risks. And insurance companies can invest their accumulated premiums in the financial markets for profit. Investment brings risks. Therefore, it is very important to explore the optimal reinsurance and investment strategy for the development of insurance companies. In this paper, the stochastic optimal control theory is mainly used. The optimal reinsurance and investment problems are solved by establishing a dynamic programming model. Firstly, reinsurance is introduced into the diffusion risk model. When the insurance company invests surplus in the risk assets and risk-free assets described by the constant elasticity variation (CEV) model, Using the principle of dynamic programming to obtain the HJB equation satisfying the value function with the goal of maximizing expected utility, then using the Legendre variable-duality method under different utility function criteria. The optimal reinsurance and investment strategy are obtained. Finally, the relationship between the relevant parameters and the optimal reinsurance investment strategy is analyzed with numerical images.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.4;F224;O212.1

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