Equilibrium pricing under relative performance concerns

Jana Bielagk (), Arnaud Lionnet () and Gonçalo dos Reis
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Jana Bielagk: HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
Arnaud Lionnet: MATHRISK - Mathematical Risk handling - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées
Gonçalo dos Reis: School of Mathematics - University of Edinburgh - The University of Edinburgh

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Abstract: We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). Each agent is not only exposed to financial and non-financial risk factors, but she also faces performance concerns with respect to the other agents. Within our proposed model we prove the existence and uniqueness of an equilibrium whose analysis involves systems of fully coupled multi-dimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a non-standard aggregation of risk measures is possible via weighted-dilated infimal convolution. We analyze the impact of the problem's parameters on the pricing mechanism, in particular how the agents' performance concern rates affect prices and risk perceptions. In extreme situations, we find that the concern rates destroy the equilibrium while the risk measures themselves remain stable.

Keywords: multidimensional quadratic BSDE; representative agent; equilibrium pricing; performance concerns; social interactions; Financial innovation (search for similar items in EconPapers)
Date: 2015-12-19
New Economics Papers: this item is included in nep-mic
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