Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

TL;DR

This paper develops stability estimates and analytic expansions for local solutions of multi-dimensional quadratic BSDEs, applying these to a financial model to analyze price stability and small risk aversion effects.

Contribution

It introduces new stability estimates and analytic expansion techniques for quadratic BSDEs, with applications to a price impact financial model.

Findings

Prices are stable under the demand process.

Analytic expansions are derived for small risk aversion coefficients.

The model provides insights into price behavior with exogenous demand.

Abstract

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analytic expansions for small risk aversion coefficients of the dealer.