Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura; Georgiy Shevchenko; Esko Valkeila

doi:10.1016/j.spa.2013.02.015

Random variables as pathwise integrals with respect to fractional Brownian motion

Yuliya Mishura^*, Georgiy Shevchenko, Esko Valkeila

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

7 Citations (Scopus)

Abstract

We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black-Scholes model of financial market.

Original language	English
Pages (from-to)	2353-2369
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	6
DOIs	https://doi.org/10.1016/j.spa.2013.02.015
Publication status	Published - 2013
MoE publication type	A1 Journal article-refereed

Keywords

Fractional Brownian motion Pathwise integral Generalized Lebesgue-Stieltjes integral Arbitrage Replication Divergence integral

Access to Document

10.1016/j.spa.2013.02.015

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Random variables as pathwise integrals with respect to fractional Brownian motion'. Together they form a unique fingerprint.

Cite this

@article{7172d28b63604da89bd4b3261246759a,

title = "Random variables as pathwise integrals with respect to fractional Brownian motion",

abstract = "We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black-Scholes model of financial market.",

keywords = "Fractional Brownian motion Pathwise integral Generalized Lebesgue-Stieltjes integral Arbitrage Replication Divergence integral",

author = "Yuliya Mishura and Georgiy Shevchenko and Esko Valkeila",

year = "2013",

doi = "10.1016/j.spa.2013.02.015",

language = "English",

volume = "123",

pages = "2353--2369",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "6",

}

TY - JOUR

T1 - Random variables as pathwise integrals with respect to fractional Brownian motion

AU - Mishura, Yuliya

AU - Shevchenko, Georgiy

AU - Valkeila, Esko

PY - 2013

Y1 - 2013

N2 - We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black-Scholes model of financial market.

AB - We give both necessary and sufficient conditions for a random variable to be represented as a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand. We also show that any random variable is a value of such integral in an improper sense and that such integral can have any prescribed distribution. We discuss some applications of these results, in particular, to fractional Black-Scholes model of financial market.

KW - Fractional Brownian motion Pathwise integral Generalized Lebesgue-Stieltjes integral Arbitrage Replication Divergence integral

UR - http://www.scopus.com/inward/record.url?scp=84875422255&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2013.02.015

DO - 10.1016/j.spa.2013.02.015

M3 - Article

AN - SCOPUS:84875422255

VL - 123

SP - 2353

EP - 2369

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 6

ER -