Actuarial Science Seminar: Optimal (re)insurance risk sharing: strategic behavior and competitive pricing

Risk sharing and optimal reinsurance arrangements have been substantially studied in the literature. Main focusses in the literature are on generalizing objective functions and incorporating more business constraints. In this talk, I will propose a bilateral risk sharing framework in reinsurance with translation invariant preferences of the agents involved. I will propose a game where insurance agents can misrepresent their risk aversion in order to alter the price. All individual rational prices constitute a Nash equilibrium. Moreover, the Stackelberg equilibria turn out to be the specific Nash equilibria where welfare gains are “allocated” to the leader of the game (typically the reinsurer, who sets the prices). I extend this idea to the case with multiple reinsurers, where the reinsurers determine the premium in a competitive manner. This leads to a specific strategic, core-type constraint, and I show the competitive prices in closed-form in case the insurance agents minimize a distortion risk measure.