Competitive Equilibria in a Comonotone Market

36 Pages Posted: 27 Dec 2017 Last revised: 20 Nov 2019

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Fangda Liu

University of Waterloo - Department of Statistics and Actuarial Science

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: December 31, 2017

Abstract

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

Boonen, Tim J. and Liu, Fangda and Wang, Ruodu, Competitive Equilibria in a Comonotone Market (December 31, 2017). 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

Ruodu Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

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