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April 2016 A system of quadratic BSDEs arising in a price impact model
Dmitry Kramkov, Sergio Pulido
Ann. Appl. Probab. 26(2): 794-817 (April 2016). DOI: 10.1214/15-AAP1103


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.


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Dmitry Kramkov. Sergio Pulido. "A system of quadratic BSDEs arising in a price impact model." Ann. Appl. Probab. 26 (2) 794 - 817, April 2016.


Received: 1 August 2014; Revised: 1 January 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1339.60071
MathSciNet: MR3476625
Digital Object Identifier: 10.1214/15-AAP1103

Primary: 60H10, 91B24, 91G80

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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