Second order stochastic target problems with generalized market impact
Abstract
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.
Cite
@article{arxiv.1806.08533,
title = {Second order stochastic target problems with generalized market impact},
author = {Bruno Bouchard and Grégoire Loeper and Halil Mete Soner and Chao Zhou},
journal= {arXiv preprint arXiv:1806.08533},
year = {2018}
}