Research On Strategies Models Of Optimal Investment And Reinsurance Of Insurance Company With The Stochastic Interest Rate

With the development of the insurance industry of our country,competition of the insurance industry is also increasingly fierce.In order to make itself invincible in the insurance industry and have long-term business,the insurance company will improve their economic strength and solvency,and invest surplus funds to make investment and reinsurance effectively.Therefore,research of the optimal investment and reinsurance strategy attracted more and more scholars' attention.At present,most researches on optimal investment and reinsurance policies are based on the fixed rate.However,the interest rate is changing over time and random variation.Therefore,traditional optimal investment and reinsurance model ignores the random characteristic of the interest rate,which is different from the practical situation.It is critical to consider the stochastic interest rate into the model,thus,providing a more accurate theoretical basis for insurance companies.Firstly,based on the study of the theoretical knowledge of interest theory,investment and reinsurance strategy and relevant literature,this article researched.Meanwhile,it is considered that the insurance company invested surplus funds in risk assets and risk-free assets under the background of fixed interest rate.This paper used proportional reinsurance way and stochastic control theory,established the corresponding HJB equation with the objective function of maximizing the probability of survival,calculated the optimal policy of optimal investment and reinsurance with the fixed interest rate by solving the corresponding equation.At the same time,the paper calculate the model numerically and analysis the influence of each parameter for policy model.Secondly,based on the model of fixed interest rate,we introduced stochastic interest rate.The stochastic interest rates are modeled by the single stochastic process,such as Wiener Process,Reflected Brownian Motion and Gauss Process.Meanwhile,the stochastic interest rates are also modeled by the quadric stochastic process,such as the combination of Poisson Process with Reflected Brownian Motion and Gauss Process respectfully.The expressions of optimal investment and reinsurance model of insurance company with the stochastic process are given.Finally,after the numerical calculations by using of Matlab,the influence from the parameters to the model of optimal investment and reinsurance strategies is analyzed,which is obtained the corresponding conclusions.It provides theoretical basis for the insurance company developing strategies of optimal investment and reinsurance.