In the Black-Scholes option pricing paradigm it is assumed that the market-mak- er designs a continuous-time hedge. This is not realistic from a practical point of view. We introduce trading restrictions in the Black-Scholes model in the sense that hedging is only allowed a given number of times-only the number is fixed, the market-maker is free to choose the (stopping) times and hedge ratios. We identify the strategy which minimizes the variance of the tracking error for a given initial value of the portfolio. The minimal variance is shown to be the solution to a sequence of optimal stopping problems. Existence and uniqueness is proved. We design a lattice algorithm with complexity N3 (N being the number of lattice points) to solve the corresponding discrete problem in the Cox-Ross-Rubinstein setting. The convergence of the scheme relies on a viscosity solution argument. Numerical results and dynamic simulations are provided
