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December 2016 First-passage times of two-dimensional Brownian motion
Steven Kou, Haowen Zhong
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Adv. in Appl. Probab. 48(4): 1045-1060 (December 2016).

Abstract

First-passage times (FPTs) of two-dimensional Brownian motion have many applications in quantitative finance. However, despite various attempts since the 1960s, there are few analytical solutions available. By solving a nonhomogeneous modified Helmholtz equation in an infinite wedge, we find analytical solutions for the Laplace transforms of FPTs; these Laplace transforms can be inverted numerically. The FPT problems lead to a class of bivariate exponential distributions which are absolute continuous but do not have memoryless property. We also prove that the density of the absolute difference of FPTs tends to ∞ if and only if the correlation between the two Brownian motions is positive.

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Steven Kou. Haowen Zhong. "First-passage times of two-dimensional Brownian motion." Adv. in Appl. Probab. 48 (4) 1045 - 1060, December 2016.

Information

Published: December 2016
First available in Project Euclid: 24 December 2016

zbMATH: 1358.60084
MathSciNet: MR3595765

Subjects:
Primary: 60J65
Secondary: 91B28

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 4 • December 2016
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