First-passage times of two-dimensional Brownian motion
2016 ◽
Vol 48
(4)
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pp. 1045-1060
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Keyword(s):
AbstractFirst-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 the 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.
2012 ◽
Vol 136
(17)
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pp. 175103
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2016 ◽
Vol 296
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pp. 275-292
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Keyword(s):
Keyword(s):
1952 ◽
Vol 211
(1106)
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pp. 431-443
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2012 ◽
Vol 82
(1)
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pp. 165-172
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2008 ◽
Vol 77
(1)
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pp. 64-71
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