Frequent hedging under transaction costs and a nonlinear Fokker-Planck PDE

We examine a commonly used model for hedging an option in markets with transaction costs. The hedging strategy in this model basically minimizes the variance of the portfolio in each time step. We show that the limiting ( number of revision intervals tending to infinity, while the level of transaction costs remains constant) PDE, governing the transaction costs, is a well-known nonlinear Fokker-Planck equation. We examine its behavior in detail, thereby obtaining that the transaction costs in this model remain finite if the size of the hedging interval tends to zero. In addition, we compare the model with a utility-based approach.