Second order stochastic target problems with generalized market impact
Bouchard, Bruno; Loeper, Grégoire; Soner, Halil Mete; Zhou, Chao (2019), Second order stochastic target problems with generalized market impact, SIAM Journal on Control and Optimization, p. 27
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
SIAM - Society for Industrial and Applied Mathematics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chaire de finance quantitative [FiQuant]
Soner, Halil Mete
Department of Mathematics [Singapore]
Abstract (EN)We extend the study of [7, 18] to stochastic target problems with general market impacts. Namely, we consider a general abstract model which can be associated to a fully nonlinear parabolic equation. Unlike [7, 18], the equation is not concave and the regularization/verification approach of  can not be applied. We also relax the gamma constraint of . In place, we need to generalize the a priori estimates of  and exhibit smooth solutions from the classical parabolic equations theory. Up to an additional approximating argument, this allows us to show that the super-hedging price solves the parabolic equation and that a perfect hedging strategy can be constructed when the coefficients are smooth enough. This representation leads to a general dual formulation. We finally provide an asymptotic expansion around a model without impact.
Subjects / Keywordsstochastic target problems; general market impacts
Showing items related by title and author.
Generalized stochastic target problems for pricing and partial hedging under loss constraints - Application in optimal book liquidation Bouchard, Bruno; Dang, Ngoc Minh (2013) Article accepté pour publication ou publié