A Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition

TL;DR

This paper introduces a two-layer stochastic game model to analyze reinsurance contracting and competition, revealing equilibrium conditions and strategies in a market with one insurer and two reinsurers.

Contribution

It develops a novel two-layer stochastic game framework for reinsurance markets, providing explicit equilibrium conditions and strategies for insurer and reinsurers.

Findings

Existence and uniqueness of equilibrium under certain competition degrees.

Equilibrium strategies are constant and fully characterized analytically.

Sensitivity analysis reveals how equilibrium strategies vary with market parameters.

Abstract

We propose a two-layer stochastic game model to study reinsurance contracting and competition in a market with one insurer and two competing reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional reinsurance contracts that are priced using the variance premium principle. The reinsurance contracting between the insurer and each reinsurer is modeled as a Stackelberg game. The two reinsurers compete for business from the insurer and optimize the so-called relative performance, instead of their own surplus, and their competition is settled by a noncooperative Nash game. We obtain a sufficient and necessary condition, related to the competition degrees of the two reinsurers, for the existence of an equilibrium. We show that the equilibrium, if exists, is unique, and the equilibrium strategy of each player is constant, fully characterized in semiclosed form. Furthermore, we obtain interesting sensitivity results for the equilibrium strategies through both analytical and numerical studies.