Determination Of The Best Retention In The Excess Of Loss Reinsurance

Reinsurance,in a short word,is to cover the risk of responsibility for the insurer. Reinsurance has a significant effect on dispersing the risk,keeping the operation,increasing the ability of insurance and promoting the healthy development of insurance.The profits will be reduced while the insurers share the some amount of risk of responsibility with other insurers.The study of the strategy of the retention comes from how to balance the relationship between profits and risks.Here based on improvement of references 1-2, we discuss the determination of the optimal retention in the mixture of quota share and excess of loss treaties reinsurance.First,adjustment coefficient in the model of Sparre Anderson is considered to be function of the retention of insurers in the mixture of quota share and excess of loss treaties reinsurance.We show that the insurer's adjustment coefficient arrive at the extremum point when the quota - share reinsurance premium is calculated on original terms and when the excess of loss premium is calculated according to the weighted premium principle.Second,the optimal retention of insurance companies are given in the compound Poisson model with diffuse disturbance term.Third,we learn the maximum retention of insurance by calculate the expected utility of wealth with respect to the quadratic utility function.Last,we study the optimal retention of excess of loss in terms of time-series dependent risks.