A New Algorithm to Simulate the First Exit Times of a Vector of Brownian   Motions, with an Application to Finance
  We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dimension higher than two. When at least one Brownian motion has non-zero drift, the joint density function of the first exit times in N dimensions needs to be known, or approximated. However, when the drifts are all zero, a simpler simulation algorithm is obtained without using the joint density function. 
Chiu-Yen Kao, Qidi Peng, Henry Schellhorn, Lu Zhu
math.PR