We consider the problem of an agent who faces losses over a finite time horizon and may choose to share some of these losses with a counterparty. The agent is uncertain about the true loss distribution and has multiple models for the losses. Their goal is to optimize a mean-variance type criterion with model combination under ambiguity through risk sharing.
We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to n insurers whose claims follow different compound Poisson processes. As the reinsurer is uncertain about the insurers’ claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers’ models.
We propose a reverse stress testing framework for dynamic loss models (in particular, compound Poisson processes over a finite time horizon). We define the stressed model as the probability measure under which the process satisfies the constraints and which minimizes the Kullback-Leibler divergence to the reference compound Poisson model. We solve for the stressed model and illustrate the dynamic stress testing by considering stresses on risk measure constraints such as Value at Risk.