Subgame Perfect Nash Equilibria in Large Reinsurance Markets

TL;DR

This paper models a complex reinsurance market with multiple insurers and reinsurers, using Choquet risk measures and nonlinear pricing, to analyze subgame perfect Nash equilibria and their efficiency.

Contribution

It introduces a unifying framework for reinsurance market equilibria using Choquet risk measures and characterizes subgame perfect Nash equilibria in this setting.

Findings

Characterization of equilibria in a multi-agent reinsurance market.

Extension of existing models to more general preferences and pricing.

Numerical illustration demonstrating theoretical results.

Abstract

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences represented by a general Choquet risk measure and can purchase coverage from any or all reinsurers. Each reinsurer has preferences represented by a general Choquet risk measure and can provide coverage to any or all insurers. Pricing in this market is done via a nonlinear pricing rule given by a Choquet integral. We model the market as a sequential game in which the reinsurers have the first-move advantage. We characterize the Subgame Perfect Nash Equilibria in this market in some cases of interest, and we examine their Pareto efficiency. In addition, we consider two special cases of our model that correspond to existing models in the related literature, and we show how our findings extend these previous results. Finally, we illustrate our results in a numerical example.