Blanchet, J., & Murthy, K. R. (2014). Exact Simulation of Multidimensional Reflected Brownian Motion. ArXiv. /abs/1405.6469

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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 strong simulation techniques (also known as Tolerance-Enforced Simulation) which allow us to provide a piece-wise linear approximation to RBM with (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.

Authors
Jose Blanchet, Karthyek RA Murthy
Publication date
2014/5/26
Journal
arXiv preprint arXiv:1405.6469