Perfect hedging under general price impact and market liquidity

We discuss a general super-hedging problem within a Markovian continuous time model of financial market with price impact and liquidity cost. It includes the linear impact model discussed in Bouchard et al. (2017). We provide... [ view full abstract ]

We discuss a general super-hedging problem within a Markovian continuous time model of financial market with price impact and liquidity cost. It includes the linear impact model discussed in Bouchard et al. (2017). We provide a characterization of the super-hedging price in terms of a fully non-linear parabolic equation. Under additional smoothness conditions on the payoff, it coincides with the perfect hedging price of a modified payoff, showing that these types of models essentially preserve completeness. We also provide a dual formulation in terms of an optimal control problem. Finally, we give an expansion around a model without impact and show how it can be used to build up very easily an approximating hedging strategy in the case of a small impact function.