Abstract

We propose a continuous-time framework to analyze optimal reinsurance, in which an insurer and a reinsurer are two players of a stochastic Stackelberg differential game. This allows us to determine optimal reinsurance from joint interests of the insurer and the reinsurer, which is rarely considered in the continuous-time setting. In the Stackelberg game, the reinsurer moves first and the insurer does subsequently to achieve a Stackelberg equilibrium toward optimal reinsurance arrangement. Under utility maximization criteria, we study the game problem starting from the general setting with generic utilities and random coefficients to the special case with exponential utilities and constant coefficients. Moreover, we consider the optimal structure when multiple reinsurers involved in a reinsurance chain as participants of the game.