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March 2013 Estimates of the exit probability for two correlated Brownian motions
Jinghai Shao, Xiuping Wang
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Adv. in Appl. Probab. 45(1): 37-50 (March 2013). DOI: 10.1239/aap/1363354102

Abstract

Given two correlated Brownian motions (Xt)t≥ 0 and (Yt)t≥ 0 with constant correlation coefficient, we give the upper and lower estimations of the probability ℙ(max0 ≤st Xsa, max 0 ≤st Ysb) for any a,b,t >0 through explicit formulae. Our strategy is to establish a new reflection principle for two correlated Brownian motions, which can be viewed as an extension of the reflection principle for one-dimensional Brownian motion. Moreover, we also consider the nonexit probability for linear boundaries, i.e. ℙ (Xtat+c,Ytbt+d, 0≤ tT) for any constants a, b≥0 and c,d, T >0.

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Jinghai Shao. Xiuping Wang. "Estimates of the exit probability for two correlated Brownian motions." Adv. in Appl. Probab. 45 (1) 37 - 50, March 2013. https://doi.org/10.1239/aap/1363354102

Information

Published: March 2013
First available in Project Euclid: 15 March 2013

zbMATH: 1262.60082
MathSciNet: MR3077540
Digital Object Identifier: 10.1239/aap/1363354102

Subjects:
Primary: 60J65
Secondary: 60G40

Keywords: boundary crossing probability , correlated Brownian motion , exit probability , reflection principle

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 1 • March 2013
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