Optimal Reinsurance And Optimal Investment Strategies Research Under The Delayed Risk Model

Reinsurance and investment issues are the current research hotspots of insur-ance risk theory in financial mathematics.For insurance companies,there are two important points:first is how to disperse risk,second is how to get maximum ben-efits.With more and more insurance companies engaged in venture capital activi-ties,how to choose the optimal investment strategy has attracted the attention of researchers,therefore,many scholars have conducted in depth research on it,there are two main research directions:one is that the ruin probability of the insurance company is the smallest,and the other is that the expected value of the insurance company is the largest.In any case,it is very difficult to calculate the optimal rein-surance strategy or the optimal investment strategy directly.It is usually assumed that the risk process follows a compound poisson process,so we use the dynamic programming method to calculate the optimal reinsurance strategy and investment strategy,and obtain the explicit solution of the optimal strategyThis paper focuses on the non-classical delay claim risk model which is studied in two ways.Firstly,the surplus process is approximated to a brownian motion by diffusion approximation under certain conditions,on this basis we take the minimum ruin probability as the optimization criterion,discuss the optimal reinsurance prob-lem under the principle of variance reinsurance,by using the principle of dynamic programming,we obtain explicit expression of the optimal retention risk level and minimum ruin probability,which has important reference value for insurance com-pany to disperse risk and financial stability;Secondly,we invest part of the surplus in the risk market and part of the surplus in the risk-free market.on this basis we use the maximization of the expected index utility of final wealth as the optimization criterion,and discuss the optimal investment and reinsurance strategy under the expected value premium principle.By constructing the Hamilton-Jacobi-Bellman equation,the explicit expressions of the optimal investment strategy,the optimal reinsurance strategy and the maximum exponential expected utility function are obtained.