Financial Risk Measurement And Reinsurance Optimization

Reinsurance is a new and effective risk management tool.An insurer can purchase the reinsurance contracts to effectively reduce the risk of bankruptcy due to insufficient ability to repay debts.With the development of risk management strategies,in order to balance the interests between the insurer and the reinsurer,more and more scholars have studied the optimal reinsurance problem.Many literatures consider the interests of the insurer.Based on the expectation pre-mium principle,the problem of the optimal reinsurance is studied by minimizing VaR and CTE risk measure.As we all know,the interests of the insurer and the reinsurer are conflicting.Therefore,considering the interests of the reinsurer,this paper establishes a mathematical model by minimizing VaR risk measure based on the distortion premium principle,the optimal reinsurance strategy is studied,and the specific form of the ceded loss function is given.Using MATLAB to give an example of specific analysis.Espe-cially,when the premium principle charged by the reinsurer to the insurer is the expected premium principle,the mathematical model is established by minimizing the CTE risk measure,the optimal reinsurance strategy is studied,and the specific form of ceded loss function is given.In recent years,some literatures have considered the policyholder,the insurer and the reinsurer,the interest of the insurer to solve the optimal insurance and reinsurance strat-egy,and some literatures have also considered the common interests of both the insurer and the reinsurer to solve the optimal reinsurance strategy.This paper also considers the policyholder,the insurer and the reinsurer,at the same time,taking into account the com-mon interests of both the insurer and the reinsurer,a mathematical model is established based on the distortion risk measure and the distortion premium principle.The optimal insurance and reinsurance strategies are studied,and the model is solved by using the Neyman-Pearson lemma.In particular,when the risk measure is VaR risk measure and the premium principle is the expected premium principle,we get the optimal insurance and reinsurance strategyIn the last part of this paper,based on the work of other scholars,we use the spe-cific form of the optimal ceded loss function to discuss the optimal safety loading of the reinsurance premium principle by establishing a mathematical model.Considering the interests of the reinsurer,we build a mathematical model based on the measurement of twist risk and the principle of twist premium,when the risk measure is VaR risk measure and the premium principle is the expected premium principle,our result is a generaliza-tion of other scholars' research results.When the risk measure is CTE risk measure and the premium principle is the expected premium principle,the optimal safety loading of the reinsurance premium principle is studied and discussed.