Windings of planar processes, exponential functionals and Asian options
Motivated by a common mathematical finance topic, we discuss the reciprocal of the exit time from a cone of planar Brownian motion which also corresponds to the exponential functional of Brownian motion in the framework of planar Brownian motion. We prove a conjecture of Vakeroudis and Yor (2012) co...
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Published in | Advances in applied probability Vol. 50; no. 3; pp. 726 - 742 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
01.09.2018
Applied Probability Trust |
Subjects | |
Online Access | Get full text |
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Summary: | Motivated by a common mathematical finance topic, we discuss the reciprocal of the exit time from a cone of planar Brownian motion which also corresponds to the exponential functional of Brownian motion in the framework of planar Brownian motion. We prove a conjecture of Vakeroudis and Yor (2012) concerning infinite divisibility properties of this random variable and present a novel simple proof of the result of DeBlassie (1987), (1988) concerning the asymptotic behavior of the distribution of the Bessel clock appearing in the skew-product representation of planar Brownian motion, as t→∞. We use the results of the windings approach in order to obtain results for quantities associated to the pricing of Asian options. |
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ISSN: | 0001-8678 1475-6064 |
DOI: | 10.1017/apr.2018.33 |