Research On Optimal Reinsurance Of Double Insurance Under Several Risk Models

With the rapid development of the insurance industry,reinsurance related issues have become a hot topic of widespread concern in the financial industry and academia.A single insurance business can no longer meet the needs of society,so it is of great theoretical and practical significance to study the optimal reinsurance of double insurance.In view of this,this paper mainly studies the optimal reinsurance problem of double insurance under several types of risk models.The first chapter first introduces the research significance of double insurance,the research background of risk models and the research status at home and abroad,including classical risk model,diffusion approximation risk model and jump-diffusion risk model.Secondly,it gives the relevant knowledge of risk theory,including reinsurance form,premium principle and bankruptcy probability.Finally,the main research content is summarized.The second chapter mainly studies the optimal reinsurance of mixed double insurance under the classical risk model.Firstly,the Lagrange function is established by using the mean variance principle,and the forms of reinsurance including proportional reinsurance and excess loss reinsurance are studied.Secondly,the equations satisfying the optimal proportional coefficient and the optimal retention amount are obtained and verified with a numerical example.Finally,the optimal reinsurance strategy under special circumstances is discussed.The third chapter mainly studies the double insurance optimal reinsurance under the diffusion approximation risk model.Firstly,the optimal reinsurance strategy is obtained by using two different methods:maximized adjustment coefficient and Hamilton-Jacobi-Bellman(HJB)equation.Secondly,it is found that the optimal strategies obtained by these two methods are consistent,and then the exact expression of the minimum bankruptcy probability is obtained.Finally,a numerical example is given to verify the application of the model.The fourth chapter mainly studies the optimal reinsurance of double insurance under the jump-diffusion risk model.Firstly,the double risk model with disturbance is established.Secondly,the relationship between the adjustment coefficient and the bankruptcy probability is proved,and the inequality between the optimal proportion coefficient and the optimal retention is obtained.Finally,the influence of parameters in the model on the optimal reinsurance strategy is analyzed with numerical examples.