Optimal Prevention Strategy Of The Generalized Poisson Risk Model Of Disturbance And Erlang（2） Risk Model

In the classical risk model,the claim process is Poisson process.However,mean equals variance is a very important property of Poisson’s process,so risk events and corresponding claim events can be considered to be equivalent.However,in the actual operation,insurance claims affairs of insurance companies are difficult to have such a nature,and risk events and corresponding claim events are not equivalent to a large extent.For example,when the insurance company implements the deductible system and No Claim Discount system,the risk events of the insurance company’s policy may not occur the corresponding claim events,so the number of claims in the corresponding claim events will not obey the Poisson distribution.In this way,the risk event is not equivalent to the corresponding claim event,that is,the risk event is not necessarily the claim event.In addition,in insurance claims,Poisson process refers to the occurrence of no more than one claim per unit time point.The Poisson process in a broad sense means that there is not one claim per unit time point or there are many claims.Erlang(n)refers to the fact that there are n claims occurring at a unit point in time.In order to spread the risk and realize the stable operation of insurance companies,measures such as self-insurance,self-protection,dividend sharing and prevention strategy can be considered respectively in the classical risk model to reduce the bankruptcy probability of insurance companies.Based on these studies,this paper studies the optimal prevention strategy of generalized Poisson risk model with disturbance and Erlang(2)risk model.The main content of the paper is as follows.First of all,it is considered that risk events and claims events may be unequal,which leads to deviation of actual insurance claims and random factors of asset fluctuations.A generalized Poisson risk prevention model with disturbance is established.When the claim follows the exponential distribution,the survival probability of the model with the adjustment coefficient is given by using martingale method.The expression of the optimal prevention quantity is obtained.Numerical simulation results show that the optimal amount of prevention is the same for any initial surplus.The optimal amount of prevention maximizes the probability of survival.When the disturbance keeps increasing,it will make the adjustment coefficient keep decreasing;when the adjustment coefficient keeps increasing,it will make the survival probability keep increasing;when the claim parameter keeps increasing,it will make the survival probability keep increasing.Secondly,Erlang(2)risk prevention model is established.The general expression of bankruptcy probability is obtained by integral differential equation.And when the claim process obeys exponential distribution,the concrete expression of survival probability is obtained.Then the optimal prevention quantity which maximizes the probability of survival is calculated,and it is proved that the optimal prevention quantity is not affected by surplus by calculating the optimal prevention quantity when surplus is 0 and surplus is u.Numerical simulation shows that the prevention strategy is effective in reducing the risk of insurance companies.Finally,the research results are summarized and the prospect is given.