ASMF seminar: Fangda Liu (Central University of Finance and Economics, China)
'Competitive equilibria in a comonotone market with rank-dependent utilities'
The notion of "competitive equilibria" has been a crucial consideration in risk sharing problems. A large literature is devoted to analyses of optimal risk sharing based on expected utilities in a complete market. In this work, we investigate the competitive equilibria in an incomplete market, where agents can only trade wealth allocations comonotone with the total wealth. 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 focus on establishing a pair of an equilibrium wealth allocation and an equilibrium pricing measure. We further propose an algorithm to numerically obtain a competitive equilibria based on discretization, which works for both the DU-comonotone market and the RDU-comonotone market. Results illustrate the intriguing and possibly puzzling fact that the equilibrium pricing kernel may not be counter-comonotone with the aggregate risk, which is a sharp contrast to the case of a complete market.
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