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

Dmitry Kramkov (1) , Sergio Pulido (2, 3)

1 CMU - Carnegie Mellon University [Pittsburgh]
2 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
3 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

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.

Mots clés: multi-dimensional quadratic BSDEs; stability of quadratic BSDEs; asymptotic behavior of quadratic BSDEs; liquidity; price impact

Domaines: Finance quantitative [q-fin.CP]; Probabilités [math.PR]; Gestion de portefeuilles [q-fin.PM]; Microstructure des marchés [q-fin.TR]

Dmitry Kramkov, Sergio Pulido. Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model. 2016. ⟨hal-01181147v2⟩