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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2019

Second order stochastic target problems with generalized market impact

Résumé

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.
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Dates et versions

hal-01820493 , version 2 (21-06-2018)
hal-01820493 , version 1 (17-12-2019)

Identifiants

Citer

Bruno Bouchard, Grégoire Loeper, Halil Mete Soner, Chao Zhou. Second order stochastic target problems with generalized market impact. SIAM Journal on Control and Optimization, 2019, 57 (6), pp.4125-4149. ⟨10.1137/18M1196078⟩. ⟨hal-01820493v2⟩
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