Seminar by Tim Boonen

Please Note: This seminar will be given in-person.

Optimal (re)insurance risk sharing: the effect of multiple insurers or reinsurers

Risk sharing and optimal reinsurance arrangements have been substantially studied in the actuarial literature. Main focusses in the literature are on generalizing objective functions and incorporating more business-related constraints. In this talk, we will propose a bilateral risk-sharing framework in reinsurance with translation invariant preferences of the agents involved. We characterize the set of all Pareto-optimal reinsurance contracts. This is next extended to the case with multiple reinsurers and one insurer, and we assume that the reinsurers determine the premium in a competitive manner. This leads to a specific core-type constraint, and we show the competitive prices in closed-form in case the insurance agents minimize a distortion risk measure. Finally, we study the impact of multiple insurers on the optimal indemnity functions.

Specifically, we characterize Pareto-optimal risk-sharing contracts in a market with multiple insurers and one (representative) reinsurer.  In the special case of coherent risk measures, the optimal indemnity schedules are further characterized in explicit form, in terms of what can be called "worst-case probability measures". The results are illustrated using a case study of flood risk insurance in the United States.