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Exact simulation of multidimensional reflected Brownian motion

Published online by Cambridge University Press:  28 March 2018

Jose Blanchet*
Affiliation:
Columbia University
Karthyek Murthy*
Affiliation:
Columbia University
*
* Current address: Management Science and Engineering, Stanford University, 475 Via Ortega, Stanford, CA 94305, USA. Email address: jose.blanchet@stanford.edu
** Postal address: Department of Industrial Engineering & Operations Research, Columbia University, S. W. Mudd Building, 500 W. 120 Street, New York, NY 10027, USA.

Abstract

We present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance–rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2018 

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