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Windings of Planar Processes and Applications to the Pricing of Asian Options

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Submitted:

22 October 2016

Posted:

24 October 2016

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Abstract
Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, we present Spitzer's asymptotic Theorem for each case. We also relate this study to the pricing of Asian options.
Keywords: 
planar Brownian motion; complex-valued Ornstein-Uhlenbeck processes; Lévy~processes; Stable processes; windings; skew-product representation; Spitzer's Theorem; Bougerol's identity; Asian options; pricing
Subject: 
Computer Science and Mathematics  -   Applied Mathematics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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