  Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we
present discrete time formulas minimizing the mean square hedging error for
multidimensional assets. In particular, we give explicit formulas when a
regime-switching random walk or a GARCH-type process is utilized to model the
returns. Monte Carlo simulations are used to compare the optimal and delta
hedging methods.
