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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

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
SIAM Journal on Control and Optimization
Publisher
SIAM - Society for Industrial and Applied Mathematics
Pages
27
Metadata
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire
Chaire de finance quantitative [FiQuant]
Soner, Halil Mete

Zhou, Chao
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 [7] can not be applied. We also relax the gamma constraint of [7]. In place, we need to generalize the a priori estimates of [18] 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 / Keywords
stochastic target problems; general market impacts

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