Fractional stochastic differential equations with applications to finance

In this paper we use a definition of the fractional stochastic integral given by Carmona et al. (2003) in [19] and develop a simple approximation method to study quasi-linear stochastic differential equations by fractional Brownian motion. We also propose a stochastic process, namely fractional semi...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 397; no. 1; pp. 334 - 348
Main Author Nguyen Tien, Dung
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2013
Subjects
Filtering
Fractional Brownian motion
Malliavin calculus
Optimal portfolio
Stochastic differential equations
Stochastic differential equations
Optimal portfolio
Filtering
Malliavin calculus
Fractional Brownian motion
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Summary:In this paper we use a definition of the fractional stochastic integral given by Carmona et al. (2003) in [19] and develop a simple approximation method to study quasi-linear stochastic differential equations by fractional Brownian motion. We also propose a stochastic process, namely fractional semimartingale, to model for the noise driving in some financial models.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.07.062