Dynamic reinsurance via martingale transport

We formulate a dynamic reinsurance problem in which the insurer seeks to satisfy prescribed terminal moment or risk-based constraints while minimizing the $L^2$-norm of the ceded risk. As a tool for this analysis, we first use techniques from martingale optimal transport to study the auxiliary problem in which the insurer matches a given terminal distribution of the surplus process. We show that, under suitable assumptions, this auxiliary problem admits a tractable solution analogous to the Bass martingale. We then relax this condition by only requiring certain moment or risk-based constraints.