On the Malliavin approach to Monte Carlo approximation of conditional expectations

@article{Bouchard2004OnTM,
  title={On the Malliavin approach to Monte Carlo approximation of conditional expectations},
  author={Bruno Bouchard and Ivar Ekeland and Nizar Touzi},
  journal={Finance and Stochastics},
  year={2004},
  volume={8},
  pages={45-71}
}
Given a multi-dimensional Markov diffusion X, the Malliavin integration by parts formula provides a family of representations of the conditional expectation E[g(X2)|X1]. The different representations are determined by some localizing functions. We discuss the problem of variance reduction within this family. We characterize an exponential function as the unique integratedvariance minimizer among the class of separable localizing functions. For general localizing functions, we provide a PDE… CONTINUE READING

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