Dynamic reinsurance via martingale transport

TL;DR

This paper introduces a dynamic reinsurance framework using martingale optimal transport to control the insurer's surplus distribution while minimizing ceded risk, providing a tractable solution under various constraints.

Contribution

It applies martingale optimal transport techniques to develop a novel dynamic reinsurance model with explicit solutions for surplus distribution control.

Findings

Provides a tractable solution similar to the Bass martingale

Extends the model to include moment and risk-based constraints

Demonstrates the applicability of martingale transport in reinsurance optimization

Abstract

We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that, under suitable assumptions, the problem admits a tractable solution analogous to the Bass martingale. We first consider the case where the insurer wants to match a given terminal distribution of the surplus process, and then relax this condition by only requiring certain moment or risk-based constraints.