The Optimal Retrospective Reinsurance Rating Plan Under Different Ceded Functions

Retrospective premium is a premium rating plan that relies on the actual loss of the insurer during the policy period.It underwrites the losses that have occurred in the period.It is an insurance plan widely used in liability insurance.But there is less literature on retrospective premium.Reinsurance is an effective method used by insurance companies to control their losses.How to design an optimal reinsurance plan is not only a hot topic in the field of actuarial science,but also a question of great interest in the fields of mathematics and statistics.This paper applies the principle of retrospective premium to the optimal reinsurance problem,then solves more reinsurance problems.First of all,the research background,current situation and significance of reinsurance issues are introduced,and the general process of reinsurance model is also explained.It also list commonly used premium principles,optimal criteria and the principle of retrospective premiums in detail.Explained both the definition of retrospective premium and the determination of its parameters,and several commonly used sets of the ceded functions are introduced at the same time.For the case that the ceded function satisfied Lipchitz continuous,and the optimal criterion is selected to minimize the risk-adjustment value,where the risk capital is measured by TVa R,the optimal ceded function under this model is in the form of stop-loss reinsurance,which is a convex function.Proved by calculation,the method to solve the optimal retention is given,and also gives examples by assuming that the risk obeys the exponential distribution,the Pareto and Gamma distribution.Through numerical simulation,the effect of the tax multiplier and the parameter on the optimal retention and the minimum risk adjustment value is explored.When other parameters are constant, increases,then the optimal retention increases and the risk adjustment value decreases.But when other parameters are constant,both the optimal retention and the minimum risk adjustment value will increase with the increase of .In addition,the expected utility that also preserves the convex order is selected as the optimal criterion,and the optimal retention of the maximum expected utility are found,then the linear utility function and the exponential utility function are selected for explanation.Most studies on optimal reinsurance problems restrict the ceded function to the set of convex functions.In practical applications,reinsurance contracts usually involve a limit on the ceded function.This article focuses on the ceded function being an increasing concave function.When the optimal criterion is selected as the value at risk(Va R),the form of the optimal ceded function under this reinsurance model is found,and the minimum VaR is calculated.By applying the principle of retrospective premium to the research of optimal reinsurance,the research conclusions on reinsurance issues are enriched and the theoretical basis is provided for practical applications in the future.