Equilibrium pricing under relative performance concerns

TL;DR

This paper models how social interactions and performance concerns among agents influence equilibrium pricing of derivatives on non-tradable assets using advanced risk measures and BSDEs, revealing conditions under which equilibrium can be disrupted.

Contribution

It introduces a novel equilibrium framework incorporating performance concerns via convex dynamic risk measures and extends the theory of risk aggregation through infimal convolution.

Findings

Performance concern rates significantly affect prices and risk perceptions.

Extreme concern levels can destroy equilibrium stability.

The model demonstrates existence and uniqueness of equilibrium under complex risk interactions.

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.