A Monte Carlo method for the simulation of first passage times of diffusion processes
type: Item
instance of: scholarly article
title: A Monte Carlo method for the simulation of first passage times of diffusion processes
zbMATH Open document ID: 1002.60066
DOI: 10.1023/A:1012261328124
author: Maria Teresa Giraudo
author: Laura Sacerdote
author: Cristina Zucca
published in: Methodology and Computing in Applied Probability
publication date: 2002-08-20T00:00:00Z
review text: The authors consider a diffusion process satisfying a one-dimensional time-homogeneous stochastic differential equation of Itô-type. They are interested in determining via a numerical approximation the first passage time, that is the first time the diffusion process reaches an absorbing boundary. The proposed numerical method is a nested Monte Carlo algorithm in the following sense. The outer ``loop'' consists of simulating (with a strong scheme such as the Milstein scheme) \(N\) trajectories of the process on a grid on the interval of interest. If a trajectory has passed the boundary on one of the subintervals of the grid, its first passage time is estimated to be the middle of the subinterval, and a new trajectory is started. The inner ``loop'' on each subinterval is required to account for undetected crossings that may occur inside it. A suitable tied-down process is introduced and the probability of it crossing the boundary is determined using a Monte Carlo method on the tied-down process. An analysis of the algorithm is carried out and the advantages of the new method compared with previously proposed methods are discussed. Finally, numerical examples are presented.
reviewed by: Evelyn Buckwar
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1784512
zbMATH Keywords: diffusion processes
zbMATH Keywords: first exit times
zbMATH Keywords: Monte Carlo methods
zbMATH Keywords: tied down processes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1784512