Equilibrium Pricing Under Relative Performance Concerns

We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on nontradable 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 (BSDEs). Each agent not only is exposed to financial and nonfinancial 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 multidimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a nonstandard 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.