Optimal Reinsurance Design under the Moment-Based Premium Principle: A Representative Reinsurer’s Perspective

Abstract. This paper investigates the optimal reinsurance problem between one insurer and multiple reinsurers, where each reinsurer prices the contract based on the first two moments of the ceded loss, and the insurer aims to minimize a distortion risk measure. We provide a representative reinsurer’s perspective to solve the problem; the representative reinsurer’s premium principle admits an analytical form and possesses the properties of monotonicity and convexity. This allows us to use a convex programming approach to numerically solve the main problem. If all the reinsurers apply the same safety loading factor for the first moment of the ceded loss in their premium principles, the representative reinsurer’s premium principle also relies only on the first two moments of the ceded loss. This significantly reduces the complexity of the original problem, allowing us to use a quadratic programming approach to find the solution.