From planar Brownian windings to Asian options
type: Item
instance of: scholarly article
title: From planar Brownian windings to Asian options
zbMATH Open document ID: 0792.60074
DOI: 10.1016/0167-6687(93)90531-S
author: Marc Yor
published in: Insurance Mathematics \& Economics
publication date: 1994-04-26T00:00:00Z
review text: The main purpose of the paper is to explain the relation between the distribution of the winding number \(\theta_ t\), \(t>0\), of planar Brownian motion around 0 and the distribution of \(A_ t^{(\nu)}=\int^ t_ 0 \exp 2(B_ s+\nu s) ds\), where \(\nu \in \mathbb{R}\) and \(B\) is a linear Brownian motion. The interest in the distribution of \(A_ t^{(\nu)}\) comes from Asian options which are functions of the time average of an asset price. Specifically the author illuminates the relationship between known formulae on transforms of \(\theta\) and \(A\) in terms of Bessel functions. The techniques used include time change, change of measure and excursion theory.
reviewed by: Michael Scheutzow
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 540711
zbMATH Keywords: Bessel process
zbMATH Keywords: complex Brownian motion
zbMATH Keywords: excursion theory
zbMATH Keywords: Asian option
zbMATH Keywords: winding number
zbMATH Keywords: change of measure
MaRDI profile type: Publication
cites work: Q3975586
cites work: Q3797994
cites work: The Laplace transform of annuities certain with exponential time distribution
cites work: BESSEL PROCESSES, ASIAN OPTIONS, AND PERPETUITIES
cites work: Excursions of Brownian motion and bessel processes
cites work: Q5332526
cites work: Q4042874
cites work: Q3215519
cites work: Q4022355
cites work: Q3923359
cites work: Some Theorems Concerning 2-Dimensional Brownian Motion
cites work: Q3997782
cites work: Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I
cites work: Q3732690
cites work: On some exponential functionals of Brownian motion
cites work: Q4693741
cites work: Q4012542
full work available at URL: 0167-6687(93)90531-s
OpenAlex ID: W2058461785
description: scientific article; zbMATH DE number 540711