SIMULATION OF FORWARD-REVERSE STOCHASTIC REPRESENTATIONS FOR CONDITIONAL DIFFUSIONS

• 成果类型: Article
• 署名作者: Bayer, Christian; Schoenmakers, John
• 署名单位: Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP969
• 发表日期: 2014
• 页码: 1994-2032
• 关键词: differential-equations

摘要

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.