Optimal Truncated Stop-loss Reinsurance Strategy Under VaR And CTE Risk Measure

Reinsurance is an important way of risk management to insurers.The choice of reinsurance strategy is of much importance for both insurers and the industry.Many researches have illustrated that stop-loss reinsurance,change-loss reinsurance,limited and truncated stop-loss reinsurance are optimal under certain conditions.Truncated stop-loss reinsurance is more economic,could reduce moral hazard and concerns about middle risk,which has larger probability to happen than extreme risk.However,since it is new,the related researches are few.In this paper,we take truncated reinsurance into account,using well-used risk measure VaR and CTE to deduct the optimal strategy.In the research under VaR principle,we find out that given the confidence interval of insurer,the safety load of reinsurer and the distribution of loss,there always exists an optimal solution for truncated stop-loss reinsurance.This paper illustrates the solution into equations,which is helpful for the usage of truncated stop-loss reinsurance in reality for the first time.We also find out that the solution is a balance between the risk of insurer and the price of reinsurance premium.In the research under CTE principle,we deducted CTE through ES(expected shortfall).And we proved that the insurer could not obtain the optimal point of CTE for the first time,which might is because of the optimal value falls at the boundary of an open set.