The Annals of Applied Probability

A system of quadratic BSDEs arising in a price impact model

Dmitry Kramkov and Sergio Pulido

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 2 (2016), 794-817.

Received: August 2014
Revised: January 2015
First available in Project Euclid: 22 March 2016

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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)

Liquidity price impact multi-dimensional quadratic BSDE


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.

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