A system of quadratic BSDEs arising in a price impact model

Dmitry Kramkov () and Sergio Pulido ()
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Dmitry Kramkov: CMU - Carnegie Mellon University [Pittsburgh]
Sergio Pulido: ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise, LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: liquidity; price impact; multi-dimensional quadratic BSDE (search for similar items in EconPapers)
Date: 2016-05-05
Note: View the original document on HAL open archive server: https://hal.science/hal-01147411v1
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Citations: View citations in EconPapers (19)

Published in The Annals of Applied Probability, 2016, 26 (2), pp.794-817

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