Competitive Equilibria in a Comonotone Market

Economic Theory, forthcoming

39 Pages Posted: 27 Dec 2017 Last revised: 1 Oct 2020

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Fangda Liu

University of Waterloo - Department of Statistics and Actuarial Science; Georgia State University

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: September 30, 2020

Abstract

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 risk allocation is comonotonic. The comonotone market is motivated by the no-sabotage condition. For instance, 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 behavioral 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 find the equilibrium in closed form in special cases. The fundamental theorems of welfare economics are established in both the DU and RDU markets. 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 comonotonicity of the pricing kernel.

Keywords: Competitive equilibria, comonotone market, dual utilities, rank-dependent utilities, pricing kernel

JEL Classification: D52, D86, G10, G22

Suggested Citation

Boonen, Tim J. and Liu, Fangda and Liu, Fangda and Wang, Ruodu, Competitive Equilibria in a Comonotone Market (September 30, 2020). Economic Theory, forthcoming, Available at SSRN: https://ssrn.com/abstract=3091424 or http://dx.doi.org/10.2139/ssrn.3091424

Tim J. Boonen

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profiel/b/o/t.j.boonen/t.j.boonen.html

Fangda Liu

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Georgia State University ( email )

35 Broad St NW
Apt 1110
Atlanta, GA 30303
United States
4703789998 (Phone)

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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