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Windings of planar processes, exponential functionals and Asian options

  • Wissem Jedidi (a1) and Stavros Vakeroudis (a2)

Abstract

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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Corresponding author

* Postal address: Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia. Email address: wissem_jedidi@yahoo.fr
** Postal address: Department of Mathematics, University of the Aegean, Vourliotis Building, Office Y5, 83200 Karlovasi, Samos, Greece. Email address: stavros.vakeroudis@gmail.com

References

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