A Note on the Distribution of Multivariate Brownian Extrema-Reference-Cited by-同舟云学术

A Note on the Distribution of Multivariate Brownian Extrema

Published:2014-11-16 Issue: Volume:2014 Page:1-6
ISSN:2090-3332
Container-title:International Journal of Stochastic Analysis
language:en
Short-container-title:International Journal of Stochastic Analysis

Author:

Escobar Marcos¹^ORCID,Hernandez Julio²

Affiliation:

1. Ryerson University, Toronto, ON, Canada M5B 2K3

2. University of Toronto, Toronto, ON, Canada M5S 2E4

Abstract

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 fundamentals 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.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Modelling and Simulation,Statistics and Probability,Analysis

Link

http://downloads.hindawi.com/archive/2014/575270.pdf

Reference16 articles.

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2. Double Lookbacks

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4. Three dimensional distribution of Brownian motion extrema

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