A note on the distribution of multivariate Brownian extrema
type: Item
instance of: scholarly article
title: A note on the distribution of multivariate Brownian extrema
zbMATH Open document ID: 1325.60079
DOI: 10.1155/2014/575270
author: Yanyan Li
published in: International Journal of Stochastic Analysis
publication date: 2015-03-27T00:00:00Z
review text: Summary: This paper presents a closed-form solution for the joint probability of the endpoints and minimums of a multidimensional Wiener process for some correlation matrices. This is the only explicit expressions found in the literature for this joint probability. The analysis can only be carried out for special correlation structures as it is related to the fundamental regions of irreducible spherical simplexes generated by reflections and the link to the method of images. This joint distribution can be used in financial mathematics to obtain prices of credit or market related products in high dimension. The solution could be generalized to account for stochastic volatility and other stylized features of the financial markets.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 91G80
zbMATH DE Number: 6420149
zbMATH Keywords: multivariate Brownian extrema
zbMATH Keywords: multidimensional Wiener process
zbMATH Keywords: correlation matrices
zbMATH Keywords: method of images
zbMATH Keywords: mathematical finance
Wikidata QID: Q59047032
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/575270
OpenAlex ID: W2076868189
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description: scientific article; zbMATH DE number 6420149