Optimal Prevention Strategy Of Double-type Insurance Risk Model And Reinsurance Risk Model

Risk theory is an important research direction of actuary.It is widely used in finance,insurance and risk management.It is a research hotspot in actuarial circles.In 1903,Filip Lundberg,a Swedish actuary,first put forward the concept of ruin probability in his doctoral thesis,which laid the theoretical foundation of risk theory.Then,based on Filip Lundberg’s work,H earald Cramer improved and standardized the classical risk model and improved the probability basis of the risk model.With the research of risk theory,the risk model is becoming more and more mature and systematicIn order to diversify risk,reduce the probability of insolvency and achieve stable operations,measures such as reinsurance strategies and preventive strategies can be considered in classical risk models.Reinsurance is a type of insurance in which the insurer transfers some of the risks and liabilities assumed by the original insurer to the remaining insurers.Preventive strategies,on the other hand,can reduce the number of claims by investing a portion of the premium in prevention,thus allowing for an optimal preventive strategy that minimises the probability of insolvency and provides security for the insurer’s operations.In the actual operation of insurance companies,there will be some random factors that make the value of insurance assets fluctuate.In view of this situation,Brown motion can be introduced into the risk model as an interference term to represent the uncertain expenditure and income of insurance companies in daily operation.The classical risk model only discusses the bankruptcy probability when operating a single insurance product.However,with the increasing expansion of the business scale of insurance companies,the diversification of insurance types and the continuous development of new insurance types,the risk model of a single insurance type can not well describe the actual situation of insurance companies,and different insurance types of insurance companies will also affect each other.Therefore,the research on double insurance types and even multiple insurance types has emerged,for the double insurance risk model related to claim,the model can be transformed into a single insurance risk model according to the additivity of Poisson process.In the classical risk model,Poisson process is generally used to describe the arrival process of claims,but in the actual insurance operation,the claim counting process is often difficult to obtain the consistent result of variance expectation,and the actual number of claims is often less than the number of accidents.For this kind of situation,the compound Poisson geometric process can be used to describe this kind of situation,and the deviation parameter can be used to represent the deviation range of the number of accidents and the actual number of claims.This process not only retains many good properties of Poisson process,such as independent increment,but also solves the problem of inconsistency between claim events and risk events.Based on the above research,this paper extends the classical risk model and studies the optimal prevention strategy under two kinds of risk models.The main contents of this paper are as follows.Firstly,due to the interaction between two types of insurance in insurance practice,which may affect the survival probability and the optimal prevention strategy,this paper establishes a claim related dual insurance risk model with prevention strategy,which is transformed into an independent dual insurance risk model by recombining the claim counting process.In order to facilitate the calculation,we assume that the two claim processes obey the exponential distribution,and obtain the exact expression of the adjustment coefficient of the model.The survival probability with surplus of 0 is obtained by using Integro-Differential Equation,and then the optimal prevention strategy to minimize the ruin probability under the model is obtained.The Lundberg Cramer approximation of the survival probability with the surplus as an arbitrary value is derived,and the optimal prevention amount image under different surplus is drawn.In the image,it can be seen intuitively that the optimal prevention amount is not affected by the change of surplus.Secondly,because the actual number of claims in the actual insurance operation is often less than the number of accidents,resulting in the deviation of insurance compensation,this paper establishes the reinsurance compound Poisson geometric risk model with prevention strategy,obtains the accurate expression of the adjustment coefficient of the model,and uses the martingale method to give the survival probability of the model with adjustment coefficient under the exponential distribution of claims,Then,the optimal prevention quantity that maximizes the survival probability under the model is calculated.By calculating the optimal prevention quantity when the surplus is 0 and the surplus is u,it is proved that the optimal prevention quantity is not affected by the surplus.Finally,the effects of reinsurance strategy and deviation parameters on survival probability are studied by numerical simulation,and relevant explanations are given.Finally,the research results of this paper are summarized,and the conclusions and prospects of this paper are given.