A system of quadratic BSDEs arising in a price impact model

TL;DR

This paper models asset prices influenced by an exogenous demand using a system of quadratic BSDEs, establishing unique solutions under certain risk-aversion conditions, and is the first to prove such global uniqueness for fully coupled systems.

Contribution

It introduces a novel approach to characterize asset prices via quadratic BSDEs and proves the first global uniqueness result for fully coupled systems.

Findings

Unique solutions exist for bounded demand when risk-aversion is small.

The system admits a unique solution in the natural class without extra norm restrictions.

First proof of global uniqueness for a fully coupled quadratic BSDE system.

Abstract

We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best of our knowledge, this is the first study that proves such (global) uniqueness result for a system of fully coupled quadratic BSDEs.