  In this work, we introduce a Monte Carlo method for the dynamic hedging of
general European-type contingent claims in a multidimensional Brownian
arbitrage-free market. Based on bounded variation martingale approximations for
Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and
constructive methodology which allows us to compute pure hedging strategies
w.r.t arbitrary square-integrable claims in incomplete markets. In particular,
the methodology can be applied to quadratic hedging-type strategies for fully
path-dependent options with stochastic volatility and discontinuous payoffs. We
illustrate the method with numerical examples based on generalized
Follmer-Schweizer decompositions, locally-risk minimizing and mean-variance
hedging strategies for vanilla and path-dependent options written on local
volatility and stochastic volatility models.
