Simulation of conditional diffusions via forward-reverse stochastic representations
- Bayer, Christian
- Schoenmakers, John G. M.
2010 Mathematics Subject Classification
- 65C05 65C30
- Forward-reverse representations, pinned diffusions, conditional diffusions, Monte Carlo simulation
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 et al. [Bernoulli, 10(2):281-312, 2004] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, 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.
- Ann. Appl. Probab., 24 (2014) pp. 1994--2032