Department seminar by Fangda Liu, Vrije Universiteit BrusselExport this event to calendar

Friday, January 19, 2018 — 1:30 PM EST

Competitive Equilibria in a Comonotone Market


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 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 focus on establishing a pair of an equilibrium wealth allocation and an equilibrium pricing measure. For DU-comonotone markets, we nd the equilibrium in closed-form. 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, in sharp contrast to the case of a complete market.

Location 
M3 - Mathematics 3
Room: 3127
200 University Avenue West
Waterloo, ON N2L 3G1
Canada

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