Optimal reinsurance from an optimal transport perspective
利用最优传输中的随机化思想和证明技巧，研究最优再保险问题，为经典结果提供新证明并建立新最优性结论。
We use the randomization idea and proof techniques from optimal transport to study optimal reinsurance problems. We start by providing conditions for a class of problems that allow us to characterize the support of optimal treaties, and show how this can be used to deduce the shape of the optimal contract, reducing the task to an optimization problem with finitely many constraints, for which standard techniques can be applied. For a more general class of problems, we regard the optimal reinsurance problem as an iterated optimal transport problem between a (known) initial risk exposure of the insurer and an (unknown) resulting risk exposure of the reinsurer. The proposed approach provides a general framework that encompasses many reinsurance problems, which we illustrate in several concrete examples, providing alternative proofs to classical optimal reinsurance results, as well as establishing new optimality results, some of which contain optimal treaties that involve external randomness.