Pareto-optimal insurance under robust distortion risk measures

This paper delves into the optimal insurance contracting problem from the perspective of Pareto optimality. The potential policyholder (PH) and finitely many insurers all apply distortion risk measures for insurance negotiation and are assumed to be ambiguous about the underlying loss distribution. Ambiguity is modeled via sets of probability measures for each agent, and those sets are generated through Wasserstein balls around possibly different benchmark distributions. We derive the analytical forms of the optimal indemnity functions and the worst-case survival functions from all the parties’ perspectives. We illustrate more implications through numerical examples.