On the first passage problem for correlated Brownian motion

Adam Metzler

Statistics & Probability Letters, 2010, vol. 80, issue 5-6, 277-284

Abstract: Suppose that X=(X1,X2) is two-dimensional correlated Brownian motion. Let [tau]i denote the first passage time of Xi to a fixed level, and [tau] the minimum of [tau]1,[tau]2. When X has zero drift, several distributions of interest are available in closed form, including the joint density of the passage times and the distribution of X([tau]). Unfortunately these published formulae contain errors, and the corresponding distributions in the presence of drift are not expressible in closed form. The purpose of this paper is to address these issues by presenting corrected formulae and outlining a Monte Carlo algorithm for approximating quantities of interest in the presence of drift.

Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00418-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:80:y:2010:i:5-6:p:277-284

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().