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We regard the optimal reinsurance problem as an iterated optimal transportproblem between a (known) initial and an (unknown) resulting risk exposure ofthe insurer. We also provide conditions that allow to characterize the supportof optimal treaties, and show how this can be used to deduce the shape of theoptimal contract, reducing the task to a finite-dimensional optimizationproblem, for which standard techniques can be applied. The proposed approachprovides a general framework that encompasses many reinsurance problems, whichwe illustrate in several concrete examples, providing alternative proofs ofclassical optimal reinsurance results as well as establishing new optimalityresults, some of which contain optimal treaties that involve externalrandomness.

Optimal reinsurance from an optimal transport perspective