Research On Optimal Reinsurance Strategy With Default Risk

Insurance industry has become an important pillar industry of national econo-my and social security,which plays an irreplaceable role in risk control and manage-ment and maintaining the stability of the financial system.Compared with other industries,insurance industry is special in that the products(or services)operated by the insurance industry are risk management and control,The insurer itself has great uncertainty in enterprise benefit,operating profit and other aspects,that is,risk.The emergence of reinsurance mechanism provides strong technical support for the insurer to effectively avoid risk and manage risk.This is also the reason why reinsurance mechanism plays an important role in the insurance industry.In this paper,three factors that must be considered in the reinsurance research,namely,the set of permitted ceding loss function,premium principle and risk mea,surement,are combed,the optimal reinsurance strategies under different sets of permitted ceding loss function are summarized,the nature of each mainstream pre-mium principle is compared,and several risk measures are introduced.Under the condition of market economy,it is possible to default if there is risk.In the reinsurance mechanism,there will also be default.In this paper,the default behavior is analyzed.According to the definition of default behavior,the mathe-matical expression of default behavior is proposed,and then the optimal reinsurance model with default risk is studied.On the basis of predecessors,this paper extends the premium principle to the generalized premium principle,and studies the optimal reinsurance model with de-fault risk based on VaR risk measurement.Since the model is an infinite dimension-al optimization model,this paper reduces the unlimited dimensional optimization model to a two-dimensional optimization model by a lemma,An optimal reinsur-ance policy with two unknown parameters is obtained.Finally,when the premium principle is specific to the distorted premium principle and the Dutch premium prin-ciple,by solving the two-dimensional optimization model,the specific values of the two unknown parameters are obtained,and the specific expression of the optimal reinsurance policy under the model is obtained.Considering that in the reinsurance mechanism,the insurer and the reinsurer are a kind of game relationship with different interests,it is necessary to study the optimal reinsurance strategy with default risk from the perspective of the reinsurer,In this paper,the optimal reinsurance model with default risk is studied from the point of view of reinsurer.An optimal reinsurance strategy with unknown parame-ters is obtained.Finally,the expression of optimal reinsurance strategy is proposed when the premium principle is specific to the expected premium principle and index premium principle.The results show that the optimal reinsurance strategy with default risk is quite different from the optimal reinsurance strategy without default risk,which reflects that default risk has a great influence on the optimal reinsurance strategy.At the same time,the optimal reinsurance strategy with default risk from the insurer's perspective is quite different from the optimal reinsurance strategy with default risk from the reinsurer's perspective,At the same time,the results of this paper have guiding significance for the insurer and reinsurer to carry out business.