Simulation of diffusions by means of importance sampling paradigm

Details Simulation of diffusions by means of importance sampling paradigm Simulation of diffusions by means of importance sampling paradigm

2010-10-21

arxiv.org/abs/1010.4447v1

Annals of Applied Probability 2010, Vol. 20, No. 4, 1389-1424

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP659 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP659

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation of diffusions when one has to consider complex boundary conditions. The method provides also an interesting alternative to performing variance reduction techniques and simulating rare events.

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