A Study Of The Minimization Of Absolute Bankruptcy Probability When Controlled By Investment And Proportional Reinsurance Under Diffusion Models

For insurance company,we assume that the surplus process is represented by a pure diffusion in this thesis.The company can invest its surplus into a Black-Scholes risky asset and risk free asset for more profit.The insurance company can in addition buy proportional reinsurance to reduce the risk of company.Combined with the existing bankruptcy theories and the actual situation,we defines a new stopping time as bankruptcy time,and the ruin probability of the bankrupt-cy time is defined as absolute ruin probability.For the independent and negative correlation of the company’s compensation risk and investment risk,we study the minimization of absolute ruin probability and the optimization strategy of investment and proportional reinsurance.By dynamic programming principle,we can obtain the corresponding HJB(Hamilton-Jacobi-Bellman)equation.Then by dividing and analyzing different control areas,the second-order differential equation of value function and the optimal investment-reinsurance strategy are obtained in different regions.Further,by comparing the stopping time with the region boundary,the second-order differential equations is optimized.Finally,the explicit expressions of minimizing absolute ruin function and the corresponding optimal investment and proportional reinsurance functions are obtained by solv-ing equations in different regions.The structure of the thesis is as following:In the first chapter,the thesis mainly introduces the principle of dynamic programming and the research background of minimizing ruin probability in risk theories.In the second chapter,assuming that the company’s risk of payment and investment risk have negative correlation,we study the problem of minimization absolute ruin probability and the cor-responding optimal investment and proportional reinsurance.By dynamic programming principle,we obtain the corresponding HJB equation.The explicit expressions of the minimizing absolute ruin probability function and the corresponding optimal investment and proportional reinsurance functions are obtained by solving HJB equation.At last,the conclusions are analyzed through numerical examples.In the third chapter,assuming that the company’s risk of payment and investment risk is independent,we study the problem of minimization absolute ruin probability and the correspond-ing optimal investment and proportional reinsurance.The explicit expressions of the minimizing absolute ruin probability function and the corresponding optimal investment and proportional rein-surance functions are obtained and the conclusions are analyzed through numerical examples.