Risk-minimizing reinsurance with adverse selection

Ka Chun Cheung, Sheung Chi Phillip Yam, Fei Lung Yuen and Yiying Zhang

Papers from arXiv.org

Abstract: This paper provides a comprehensive characterization of optimal reinsurance mechanisms under adverse selection when a monopolistic reinsurer faces a continuum of insurers with multi-dimensional private information on loss exposures and Value-at-Risk (VaR) preferences. Moving beyond standard single-dimensional or discrete-type models, we resolve an infinite-dimensional, non-convex screening problem by introducing a novel pre-reinsurance VaR reparameterization and an indirect utility representation. This framework converts global incentive constraints into tractable, typewise conditions. Using a Breeden-Litzenberger representation, we show that optimal indirect utility consistently adopts a hinge form across stop-loss, quota-share, and change-loss contract classes, yielding an endogenous market-exclusion threshold. Among participating types, stop-loss contracts screen via type-dependent deductibles, whereas quota-share contracts induce complete pooling at full coverage. Moreover, under mild conditions, expanding the contract space to change-loss policies yields no extra profit beyond optimal stop-loss designs. Numerical examples further illustrate the fundamental economic trade-off between extracting information rents and excluding low-exposure types. Our approach provides deeper insight into the mechanisms of discrimination and exclusion in reinsurance markets characterized by asymmetric information, enriching theoretical and practical perspectives on contract design in the presence of adverse selection.

Date: 2025-04, Revised 2026-09
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