Competitive equilibria in a comonotone market
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Competitive equilibria in a comonotone market Tim J. Boonen1
· Fangda Liu2
· Ruodu Wang2
Received: 3 June 2020 / Accepted: 6 October 2020 © The Author(s) 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.
Fangda Liu is supported by the NNSF of China (No. 11601540) and the Natural Sciences and Engineering Research Council of Canada (RGPIN-2020-04717, DGECR-2020-00340). Ruodu Wang is supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2018-03823, RGPAS-2018-522590).
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Tim J. Boonen [email protected] Fangda Liu [email protected] Ruodu Wang [email protected]
1
Amsterdam School of Economics, University of Amsterdam, Amsterdam, The Netherlands
2
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
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T. J. Boonen et al.
Keywords Competitive equilibria · Comonotone market · Dual utilities · Rank-dependent utilities · Pricing kernel JEL Classification D52 · D86 · G10 · G22
1 Introduction 1.1 Background This paper studies risk sharing games in a special type of one-period exchange markets, called the comonotone markets, and compare them with those in the classic complete markets. A comonotone market is one in which only comonotonic risk allocations (defined in Sect. 2) are allowed. Equivalently, market participants only trade risk allocations in the market that are comonotonic with the market total risk. This may be interpreted as, for instance, the market total risk is the systematic risk that is present, and participants are not allowed to bet against it. Comonotone markets are closely related
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