UNBIASED SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS
成果类型：
Article
署名作者：
Henry-Labordere, Pierre; Tan, Xiaolu; Touzi, Nizar
署名单位：
Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/17-AAP1281
发表日期：
2017
页码：
3305-3341
关键词：
摘要：
We propose an unbiased Monte 3 estimator for E [g(X-t1,..., X-tn)], where X is a diffusion process defined by a multidimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regime-switching SDE, or as a branching diffusion process with one single living particle at all times. In order to compensate for the change of the coefficients of the SDE, our main representation result relies on the automatic differentiation technique induced by the Bismut-Elworthy-Li formula from Malliavin calculus, as exploited by Fournie et al. [Finance Stoch. 3 (1999) 391-412] for the simulation of the Greeks in financial applications. In particular, this algorithm can be considered as a variation of the (infinite variance) estimator obtained in Bally and Kohatsu-Higa [Ann. Appl. Probab. 25 (2015) 3095-3138, Section 6.1] as an application of the parametrix method.
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