Exact Simulation of Multidimensional Reflected Brownian Motion

TL;DR

This paper introduces the first exact simulation method for multidimensional reflected Brownian motion, overcoming previous challenges by combining epsilon-strong simulation techniques with a novel acceptance/rejection step.

Contribution

It develops a new exact simulation approach for multidimensional RBM using epsilon-strong simulation and a conditional acceptance/rejection mechanism.

Findings

First exact simulation method for multidimensional RBM

Achieves epsilon-approximate piece-wise linear approximation

Eliminates approximation error through a novel rejection step

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