  We study a reinsurer who faces multiple sources of model uncertainty. The
reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson
processes representing both idiosyncratic and systemic sources of loss. 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 apply our results to
proportional reinsurance and excess-of-loss reinsurance contracts, and
illustrate the solutions numerically. Furthermore, we solve the related problem
where the reinsurer maximises, still under ambiguity, their expected utility
and compare the solutions.
