Journal
ANNALS OF APPLIED PROBABILITY
Volume 24, Issue 5, Pages 1994-2032Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AAP969
Keywords
Forward-reverse representations; pinned or conditional diffusions; Monte Carlo simulation
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Funding
- DFG Research Center MATHEON Mathematics for Key Technologies in Berlin
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In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers and Spokoiny [Bernoulli 10 (2004) 281-312] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, and hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset.
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