The Optimal Reinsurance Under The Variable Transformation Method And MIF Function

Reinsurance is a risk management tool for insurance company,By balancing ceded loss and reinsurance premium,an insurer can control its risk by ceding part of its risk to reinsurer.The measure of optimal reinsurance standards can be divided into the following three categories: minimizing variance,maximizing the utility function minimizing and the probability of ruin.In recent years,many scholars to study the optimal reinsurance with risk measure.So we research the optimal reinsurance by risk measure.The main contents are summarized as follows:The measure of optimal reinsurance standards can be divided into the following three categories: to maximize the utility function to minimize the ruin probability and risk minimization.In recent years,many scholars to study the optimal reinsurance measure risk.The first chapter introduces the research background and the present situation of reinsurance,then,introduces the research content of this paper.The second chapter introduces the definition of reinsurance,several common premium principles and risk measures.The third chapter,we take the stop-loss reinsurance as the research object.Under the VaR and CTE risk measures,we propose a variable transformation way and obtain the optimal stop-loss reinsurance under value at risk(VaR)and conditional tail expectation(CTE)criteria,respectively.Let be the initial loss of an insurer with cumulative distribution function and survival function.Denote a transformation variable.Firstly,we analyze properties of the variables and Then,under VaR-and CTE-optimization criteria,we provide the necessary and sufficient conditions for the optimal retention existence of,respectively.Further,the optimal retention of is obtained.Some examples are given to illustrate these results.The fourth chapter,we revisit the optimal reinsurance problem under the optimality criteria of VaR with considering to the effect of the reinsurer's default risk.In a reinsurance contract,a reinsurer promises to pay the part of the loss faced by an insurer by charging the insurer a certain amount of premiums.However,default risk occurs when the reinsurer undertakes to pay more than his own solvency.Therefore,it is necessary to consider the default risk.Under Wang's premium principle,It is shown that layer reinsurance is the optimal reinsurance policy over VaR risk measure.Finally,the corresponding numerical results are presented.The fifth chapter,we use the distortion risk measure and distortion premium principle to establish the total risk model with default risk.Firstly,by the relationship between the marginal claim(MIF)function and the ceded loss function.we build MIF reinsurance optimization model equivalent to total risk model.Then,the optimal MIF function is obtained by solving the MIF reinsurance optimization model,furthermore,the optimal ceded loss function is obtained.Finally,we apply this method to study the optimal loss function by the VaR risk measure and Wang's premium.The sixth chapter,the results of this paper are discussed and summarized.