Research On The Optimal Investment Strategy Problem Based On Non-proportional Reinsurance

In recent years,due to the increasingly fierce competition in the insurance market,it is more difficult to maintain the operation of insurance companies only by charging premiums.In this regard,insurance companies will choose reinsurance to share the risk,through investment to maintain and increase the value of the company.Then,how to optimize the target value by controlling investment and reinsurance strategy is the main problem faced by insurance companies.There are many valuable research results on this problem.The reinsurance of insurance companies is generally divided into proportional reinsurance and non proportional reinsurance,and one of the important reinsurance in non proportional reinsurance is excess-claim reinsurance.For insurance companies,the biggest concern is problem of insolvency.As for the concept of insolvency,a surplus of 0 is insolvency in the classical ruin theory,however,considering the actual situation,insurance companies can make up for the deficit by borrowing from banks.Absolute ruin theory defines that an insurance company will go bankrupt when the surplus is negative.However,in reality,when the deficit reaches a certain value,the company can not continue to operate because of insolvency.Therefore,in this paper,absolute ruin is defined as the surplus reaches a negative lower bound.In this paper,excess-claim reinsurance and mixed reinsurance are used as reinsurance.For the investment and reinsurance model,the absolute ruin probability is taken as the value function to be studied,the optimal investment and reinsurance strategy are studied,and the explicit solution of the optimal value function is obtained.The specific arrangements are as follows:Firstly,the research background about investment and reinsurance problem is introduced.Secondly,the insolvency of an insurance company is considered for the risk model with investment and excess-claim reinsurance.Considering the insolvency of the insurance company,the absolute ruin of the company is determined as a negative surplus by the reality.Choosing the absolute ruin probability as the value function to be studied,the corresponding HJB(Hamilton-Jacob-Bellman)equation is derived for the diffusion approximation model.By distinguishing the control areas and solving equation separately,the optimal strategy of investment and reinsurance is derived and the explicit expression of the optimal value function is obtained.We compare the results with those of investment and proportional reinsurance model.Finally,we consider the diffusion approximation model with investment and mixed reinsurance,study the same value function as in Chapter 2,and derive the equation corresponding to the value function.The optimal strategies of investment and reinsurance are obtained by solving the control areas,and then the explicit solution of the optimal value function is obtained.Finally,a numerical example is given to illustrate the effect of proportional reinsurance on excess claim reinsurance.