Reserach On Optimal Dividend Strategy And Ruin Probability Of Insurance Companies With Uncertain Income

With the gradual improvement of technology and living standards,people's awareness of insurance has also risen,so the study of related issues in the field of financial insurance has been paid more and more attention by scholars.The optimal dividend problem and ruin probability problem of insurance companies are important research contents in the field of financial insurance.Based on the previous research results,this paper considers the optimal dividend distribution of insurance companies in independent and dependent environments when operating income and uncertain non-operating income(uncertain income).Then continues to under the continuous-time compound binomial model with uncertain income,the ruin probability of insurance companies under different dividend strategies is studied.The main content can be divided into the following section s:Firstly,we introduce the insurance company's uncertain non-operating income based on the classical discrete dividend model.Under the assumption that the operating income and the uncertain non-operating income are independent,we study the optimal dividend distribution of insurance companies with uncertain returns at discrete time points.By introducing risk coefficient with the help of binary joint entropy risk measure,a diffusion dividend model is established,and the corresponding cash flow discount of dividend at each discrete time point is obtained.The optimal dividend strategy in finite time and infinite time range is studied,and prove that the band strategy is optimal.Then through numerical simulation,the influence of different risk factors on the optimal dividend strategy is analyzed.Secondly,it is assumed that the operating income of insurance companies in different periods is dependent on uncertain non-operating income.FGM Copula has been widely used in the field of risk theory and actuarial insurance because of its excellent analytical properties.So this paper uses FGM Copula to describe this dependency.By introducing risk coefficient with the help of binary joint entropy risk measure,a diffusion dividend model is established,and the corresponding cash flow discount of dividend at each discrete time point is obtained.The optimal dividend strategy with finite and infinite time is studied and it is proved that the optimal dividend strategy is a band strategy and the policy improvement algorithm can be used to obtain the optimal dividend policy and the corresponding value function.Finally,Numerical studies are given and discuss the influence of the risk parameter and correlation coefficients on the optimal dividend strategy.Thirdly,the joint distribution of ruin time,the surplus before ruin and the deficit at ruin in the continuous-time compound binomial model with uncertain earnings is analyzed.Then the ruin probability problem of continuous-time compound binomial model with barrier dividends and linear dividend strategies with uncertain income terms is considered separately.And with the help of the Gerber-Shiu discount penalty function,the time of ruin,the surplus before ruin and the deficit at ruin of the model are analyzed,and correspondingly get the expression they satisfy.Finally,the research content of the full text is summarized,and points out some areas that need to be improved and can be further expanded,so as to study later.