Dynamic reinsurance via martingale transport

2026-01-15

AI Summary

This study addresses the problem of dynamic reinsurance design, wherein an insurer seeks to minimize the L²-norm of ceded risk while matching a prescribed terminal surplus distribution or satisfying moment- and risk-based constraints. To this end, the paper introduces martingale optimal transport theory—hitherto unexplored in reinsurance contexts—into the dynamic reinsurance framework, combining stochastic control with constrained optimization. This approach yields an analytically tractable optimal strategy characterized as a Bass-like martingale. The proposed methodology not only extends the classical actuarial optimization paradigm but also enables exact terminal distribution matching and accommodates more flexible risk constraints. Under reasonable assumptions, the resulting reinsurance design is both computationally manageable and highly efficient.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• dynamic reinsurance
• terminal distribution
• ceded risk
• martingale transport
• surplus process

Innovation

• martingale optimal transport
• dynamic reinsurance
• Bass martingale
• terminal distribution control
• L2-norm minimization