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1 Humboldt Universität zu Berlin Berlin 2 MATHRISK - Mathematical Risk handling Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech 3 School of Mathematics - University of Edinburgh

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 : performance concerns equilibrium pricing representative agent multidimensional quadratic BSDE social interactions Financial innovation





Author: Jana Bielagk - Arnaud Lionnet - Gonçalo Dos Reis -

Source: https://hal.archives-ouvertes.fr/



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