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Equilibria and efficiency in a reinsurance market
Journal article   Peer reviewed

Equilibria and efficiency in a reinsurance market

Michael B. Zhu, Mario Ghossoub and Tim J. Boonen
Insurance, mathematics & economics, Vol.113, pp.24-49
11/01/2023
DOI: 10.1016/j.insmatheco.2023.07.004

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Abstract

We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heteroge-neous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg setting, which assumes a single monopolistic reinsurer on the supply side, our model accounts for strategic price competition between reinsurers. We argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept for analyzing equilibria in the reinsurance market, and we characterize SPNEs using a set of sufficient conditions. We then examine efficiency properties of the contracts induced by an SPNE, and show that these contracts result in Pareto-efficient allocations. Additionally, we show that under mild conditions, the insurer realizes a strict welfare gain, which addresses the concerns of Boonen and Ghossoub (2022) with the Stackelberg model and thereby ultimately reflects the benefit to the insurer of competition on the supply side. We illustrate this point with a numerical example.& COPY; 2023 Elsevier B.V. All rights reserved.
 Business & Economics Economics Mathematical Methods In Social Sciences Mathematics Mathematics, Interdisciplinary Applications Physical Sciences Science & Technology Social Sciences Social Sciences, Mathematical Methods Statistics & Probability

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