Optimal Reinsurance Strategy Under The TVaR Risk Measure

Reinsurance,as a type of risk sharing,has been extensively studied in actuarial science.Most existing results are from the insurer's point of view.But a reinsurance contract includes insurer and reinsurer,we should consider the interests of both sides.In recent years,many scholars have been studied Pareto-optimal reinsurance policies,where both the insurer's and the reinsurer's risks and return are considered.Pareto-optimal policies can be determined by minimizing a linear combination of the two parties in the reinsurance transaction.In this paper,we aim at minimizing the convex combination of the TVaRs of the insurer's and reinsurer's total loss.The objective of this paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts:the quota share and the stop loss.Furthermore,as many as 16 reinsurance premium principles are investigated.We discuss the confidence level of the insurer and the reinsurer in the same and different two different situations.Depending on the chosen principles,optimal quota-share and stop-loss reinsurance may or may not exist.For some cases we formally establish the sufficient and necessary conditions for the existence of the nontrivial optimal reinsurance.Numerical examples are presented to illustrate our results.