Studies On Optimal Reinsurance Under VAR And CVaR

At present,with the progress of social economy,the insurance industry is also continuously developing.The study of optimal reinsurance has become one of the hot topics in the field of mathematical finance.By balancing the retained risk and reinsurance premium of insurer,the insurer chooses the best reinsurance design to minimize the risk it faces.The criteria for measuring optimal reinsurance agreements fall into the following four categories: minimization of variance,minimization of ruin probability,maximization of utility functions and minimization of risk measures.However,with the implementation of the Basel Agreement,the study of optimal reinsurance focuses on the risk measures VaR and CVaR standards.The master's thesis focuses on VaR and CVaR to study the optimal reinsurance.The concrete framework is as follows:In the first chapter,the research background,the present situation and the content of the research are introduced.In the second chapter,the basic symbols,the common premium principles,the set of admissible functions,the risk measures VaR and CVaR,and the related properties are introduced.In the third chapter,this chapter assumes that the loss functions retained by the insurer are increased,the loss functions ceded are the Vajda function,the principle of reinsurance premiums satisfy three properties: distribution invariance,risk loading and preserve stop-loss order.Then,by minimizing the total risk of insurer under VaR and CVaR,we studies two types of optimal reinsurance models.In the fourth chapter,this chapter assumes that the loss functions retained and ceded by the insurer are all increased,and the ceded loss functions are accompanied by the upper limit.Reinsurance premiums select the expected premium principle and the premium principle is accompanied by the upper limit.Then,by minimizing the total risk of the insurer under VaR and CVaR,we get a clear optimal reinsurance agreement.In the fifth chapter,in order to find the optimal retention of insurance products with deductible under the stop-loss reinsurance treaty.First,under risk measures VaR and CVaR,the article describes the optimal reinsurance model for the total loss of certain insurance products after deducting the deductible amount,and gives the optimal retention of the optimal reinsurance model.Then,given that distribution of basic loss obeys the exponential distribution,the specific form of the survival function for the total loss added to the deductible is given.Finally,the paper gives a specific numerical simulation.In the sixth chapter,we summarize the results of this article and look forward to the future work.