导　　师： 张华嘉

学科专业： 070103

授予学位： 硕士

作　　者： ;

机构地区： 暨南大学

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。 As the vigorous development of insurance industry, the market scale gradually expands andthe risk the insurance companies face increases. In order to spread the risks andstabilize operation, insurance companies need to take measures of reinsurance to transfer a partof risks out. Risk reduction must be accompanied by the apportionment of premiums, whichmean that insurance companies’ profitable capital will decrease. Therefore, insurance companiesrequire balance between benefits and risks in reinsurance. For the purpose of benefits acquisition,at the same time, insurance companies can invest a few accumulated premiums to thefinancial market to obtain a higher expected return. However, investment bring risk. It willinevitably face the decision problem about returns and risks. So it is crucial to explore theoptimal reinsurance and investment strategy for the development of insurance company. Based on stochastic optimal control theory, this paper establishes a dynamic programmingmodel to solve the optimal reinsurance and investment issues. We firstly introduce reinsurance tothe diffusion risk model. When insurance company invest its surplus to risk-free assets or riskassets which are described by constant elasticity variation /(CEV/) model, through dynamicprogramming principle we can get the HJB equation with maximizing expected utility as theobjective function. Next, in different utility functions we obtain the optimal reinsurance andinvestment strategies with Legendre change-dual approach. Finally, values and images arecombined to analyze the relationship between some related parameters and the optimalreinsurance investment strategies.

关 键 词： 随机最优控制 再保险 投资 模型 方程

分 类 号： [F840.4 F224 O212.1]

领　　域： [经济管理] [经济管理] [理学] [理学]