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Simulation of stopped diffusions

by F. Buchmann

(Report number 2004-03)

Abstract
In this work we study standard Euler updates for simulating stopped diffusions. As an immediate application we discuss the computation of first exit times of diffusions from a domain. We focus on one dimensional situations and show how the ideas for the simulation of killed diffusions can be adapted to this problem. In particular, we give a fully implementable algorithm to compute the first exit time from an interval numerically. The Brownian motion case is treated in detail and extensions to general diffusions are given.

Keywords:

@Techreport{B04_330,
  author = {F. Buchmann},
  title = {Simulation of stopped diffusions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2004-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2004/2004-03.pdf },
  year = {2004}
}

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