Equilibria and efficiency in a reinsurance market

Michael B. Zhu, Mario Ghossoub and Tim J. Boonen

Insurance: Mathematics and Economics, 2023, vol. 113, issue C, 24-49

Abstract: We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous 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.

Keywords: Optimal reinsurance; Bowley optima; Stackelberg equilibria; Subgame perfect Nash equilibria; Pareto efficiency; Choquet pricing; Heterogeneous beliefs (search for similar items in EconPapers)
JEL-codes: C02 C62 C79 D86 G22 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:113:y:2023:i:c:p:24-49

DOI: 10.1016/j.insmatheco.2023.07.004

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