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The simulation of exit times for diffusion processes is a challenging tasksince it concerns many applications in different fields like mathematicalfinance, neuroscience, reliability... The usual procedure is to usediscretiza-tion schemes which unfortunately introduce some error in the targetdistribution. Our aim is to present a new algorithm which simulates exactly theexit time for one-dimensional diffusions. This acceptance-rejection algorithmrequires to simulate exactly the exit time of the Brownian motion on one sideand the Brownian position at a given time, constrained not to have exit before,on the other side. Crucial tools in this study are the Girsanov transformation,the convergent series method for the simulation of random variables and theclassical rejection sampling. The efficiency of the method is described throughtheoretical results and numerical examples.

Exact simulation of first exit times for one-dimensional diffusion processes