Hedging of Covered Options with Linear Market Impact and Gamma Constraint

Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the superreplication price is the viscosity solution of a fully nonlinear parabolic equation. As a by-product, we show how ε-optimal strategies can be constructed. Finally, a numerical resolution scheme is proposed.