Competitive Equilibria in a Comonotone Market
36 Pages Posted: 27 Dec 2017 Last revised: 20 Nov 2019
Date Written: December 31, 2017
The notion of competitive equilibria has been fundamental to game theory and financial economics. A large portion of the literature is devoted to analyses of risk sharing games based on expected utilities and complete markets. In this paper, we investigate competitive equilibria in a special type of incomplete markets, referred to as a comonotone market, where agents can only trade such that their wealth allocation is comonotonic. The comonotone market is motivated by two seemingly unrelated observations. First, in a complete market, under mild conditions on the preferences, an equilibrium allocation is generally comonotonic. Second, in a standard insurance market, the allocation of risk among the insured, the insurer and the reinsurers is assumed to be comonotonic a priori to the risk-exchange. Two popular classes of preferences in risk management and behavioural economics, dual utilities (DU) and rank-dependent expected utilities (RDU), are used to formulate agents' objectives. We present various results on properties and characterization of competitive equilibria in this framework, and in particular their relation to complete markets. For DU-comonotone markets, we find the equilibrium in closed-form and for RDU-comonotone markets, we obtain closed-form in special cases. We further propose an algorithm to numerically obtain competitive equilibria based on discretization, which works for both the DU-comonotone market and the RDU-comonotone market. Although the comonotone and complete markets are closely related, many of our findings are intriguing and in sharp contrast to results in the literature on complete markets in terms of existence, uniqueness, and closed-form solutions of the equilibria, and monotonicity of the pricing kernel.
Keywords: Competitive equilibria, comonotone market, dual utilities, rank-dependent utilities
JEL Classification: D52, G10
Suggested Citation: Suggested Citation