UNCONSTRAINED RECURSIVE IMPORTANCE SAMPLING

• 成果类型: Article
• 署名作者: Lemaire, Vincent; Pages, Gilles
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP650
• 发表日期: 2010
• 页码: 1029-1067
• 关键词: stochastic-approximation

摘要

We propose an unconstrained stochastic approximation method for finding the optimal change of measure (in an a priori parametric family) to reduce the variance of a Monte Carlo simulation. We consider different parametric families based on the Girsanov theorem and the Esscher transform (exponential-tilting). In [Monte Carlo Methods Appl. 10 (2004) 1-24], it described a projected Robbins-Monro procedure to select the parameter minimizing the variance in a multidimensional Gaussian framework. In our approach, the parameter (scalar or process) is selected by a classical Robbins-Monro procedure without projection or truncation. To obtain this unconstrained algorithm, we extensively use the regularity of the density of the law without assuming smoothness of the payoff. We prove the convergence for a large class of multidimensional distributions as well as for diffusion processes. We illustrate the efficiency of our algorithm on several pricing problems: a Basket payoff under a multidimensional NIG distribution and a barrier options in different markets.