模糊厌恶视角下具有通货膨胀影响的鲁棒最优再保险和投资  

Robust Optimal Reinsurance and Investment with Inflation Influence from the Perspective of Ambiguity Aversion

作　　者：杨鹏 YANG Peng(School of Mathematics,Xi'an University of Finance and Economics,Xi'an 710100)

机构地区：[1]西安财经大学数学学院,西安710100

出　　处：《系统科学与数学》2024年第1期164-178,共15页Journal of Systems Science and Mathematical Sciences

基　　金：陕西省自然科学基础研究计划资助项目(2023-JC-YB-002);教育部人文社会科学研究西部和边疆地区项目青年基金(21XJC910001)资助课题.

摘　　要：文章在同时考虑模糊厌恶和通货膨胀风险下,研究鲁棒最优再保险和投资问题.保险公司的盈余过程通过扩散逼近模型定义,金融市场由一个无风险资产和风险资产组成.保险公司通过采取比例再保险减少索赔风险,通过在金融市场投资增加财富.通过通货膨胀对风险资产价格进行折算,得到通货膨胀对投资的影响.利用Radon-Nikodym导数和Girsanov定理,得到模糊厌恶下,保险公司的财富过程.以期望效用最大化为目标,得到鲁棒最优再保险和投资策略的解析解.最后,通过数值实验探讨模型参数对所得理论结果的影响,研究结果可以有效地指导保险公司的再保险和投资决策.This paper studies the robust optimal reinsurance and investment problem under the ambiguity aversion and inflation risks are considered,simultaneously.The surplus process of an insurance company is defined by the diffusion approximation model,and the financial market consists of a risk-free asset and a risky asset.The insurance company can reduce the risk of claims by adopting proportional reinsurance and increase his wealth by investing in the financial market.The price of the risky asset is converted by inflation,and then the influence of inflation on investment is obtained.By using Radon-Nikodym derivative and Girsanov theorem,the wealth process of the insurance company under ambiguity aversion is obtained.With the goal of maximizing expected utility,the analytical solution of robust optimal reinsurance and investment strategy is obtained.Finally,the influence of model parameters on the theoretical results is discussed through numerical experiments,and the research results can effectively guide the reinsurance and investment decisions of the insurance company.

关 键 词：模糊厌恶 通货膨胀 再保险 投资 随机控制 

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