Equilibria in Reinsurance Markets: Monopolistic vs. Competitive Pricing
The notion of a Bowley optimum (or Stackelberg equilibrium) has gained recent popularity as an equilibrium concept in reinsurance markets, but it assumes a monopolistic structure on the supply side. This is in contrast to reinsurance markets in which equilibrium pricing arises through strategic price competition between reinsurers. In this talk, I will discuss both market structures and argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept in the latter market setting. I will provide a characterization of equilibrium reinsurance contracts in each case, under fairly general assumptions about the preferences of market participants. Finally, I will discuss the Pareto-efficiency of equilibria and whether efficient allocations can be decentralized in each market structure. Specifically, Bowley-optimal contracts lead to Pareto-efficient allocations, but they make the insurer indifferent with the status quo. Moreover, only those Pareto-efficient contracts that make the insurer indifferent between suffering the loss and entering into the reinsurance contract are Bowley optimal. This is indicative of the limitations of Bowley optimality as an equilibrium concept. In the second market structure, equilibrium contracts induced by an SPNE result in Pareto-efficient allocations. Additionally, under mild conditions, the insurer realizes a strict welfare gain, which addresses the shortcomings of the Bowley setting and thereby ultimately reflects the benefit to the insurer of competition on the supply side.