Second order stochastic target problems with generalized market impact
Bouchard, Bruno; Loeper, Grégoire; Soner, Halil Mete; Zhou, Chao (2018), Second order stochastic target problems with generalized market impact. https://basepub.dauphine.fr/handle/123456789/17924
TypeDocument de travail / Working paper
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Soner, Halil Mete
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
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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