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Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations

Research output: Contribution to journalArticle

E. Gobet, P. Turkedjiev

Original languageEnglish
JournalStochastic Processes and Their Applications
Early online date26 Aug 2016
DOIs
Accepted/In press25 Jul 2016
E-pub ahead of print26 Aug 2016

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Abstract

We design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in least-squares Monte-Carlo (LSMC) algorithms. The Radon-Nikodym derivative depends on the solution of BSDE, and therefore it is computed adaptively within the LSMC procedure. To allow robust error estimates w.r.t. the unknown change of measure, we properly randomize the initial value of the forward process. We introduce novel methods to analyze the error: firstly, we establish norm stability results due to the random initialization; secondly, we develop refined concentration-of-measure techniques to capture the variance reduction. Our theoretical results are supported by numerical experiments.

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