Optimal Reinsurance Based On The Viewpoint Of Both An Insurer And A Reinsurer

Reinsurance plays a vital role in the insurance activities. The insurer and the reinsurer, which have conflicting interests, compose the two parties of a reinsur-ance contact. At first, we study the optimal quota-share and stop-loss reinsurance models from the perspectives of both the insurer and the reinsurer by minimizingthe convex combination of the VaR risk measures of the insurer's cost and the reinsurer's cost. Furthermore, as many as 16 reinsurance premium principles are investigated. The results show that optimal quota-share and stop-loss reinsurancemay or may not exist depending on the chosen principles. Moreover, we establishthe sufficient and necessary conditions for the existence of the nontrivial optimalreinsurance. Secondly, we obtain the Pareto-optimal policies by minimizing the convex combination of the VaR risk measures of the insurer's loss and the reinsur-er's loss. Then the optimal forms and parameter values are determined under the Wang's premium principle.