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We provide a new methodology to simulate the first exit times of a vector ofBrownian motions from an orthant. This new approach can be used to simulate thefirst exit times of dimension higher than two. When at least one Brownianmotion has non-zero drift, the joint density function of the first exit timesin N dimensions needs to be known, or approximated. However, when the driftsare all zero, a simpler simulation algorithm is obtained without using thejoint density function.

A New Algorithm to Simulate the First Exit Times of a Vector of Brownian Motions, with an Application to Finance