The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 2 (2016), 794-817.
A system of quadratic BSDEs arising in a price impact model
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.
Ann. Appl. Probab., Volume 26, Number 2 (2016), 794-817.
Received: August 2014
Revised: January 2015
First available in Project Euclid: 22 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 91B24: Price theory and market structure 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Kramkov, Dmitry; Pulido, Sergio. A system of quadratic BSDEs arising in a price impact model. Ann. Appl. Probab. 26 (2016), no. 2, 794--817. doi:10.1214/15-AAP1103. https://projecteuclid.org/euclid.aoap/1458651820