On the mixed fractional Brownian motion

By M. Zili. 2006

227 citations recorded by the source corpus.

The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the α-differentiability of its sample paths.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/675abf612e28a450440d93165801688e92f8f02a

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Citations in the corpus

Representation formulae for the fractional Brownian motion (2009, background): “As an application, we recover a result of [4], see also [2, 37] for more general results.”
Advanced Local Fractional Calculus and Its Applications (2012, background): “[61] Mounir Zili, On the mixed fractional Brownian motion, Journal of Applied Mathematics and Stochastic Analysis, ID 32435 (2006) 1-9.”
Wiener integrals, Malliavin calculus and covariance measure structure (2006, unknown): “This means in particular that for ϕ, ψ ∈ D ( R ) (the space of smooth test functions with compact support) Example 4.5 We provide now an example of a process with stationary increments, investigated for ﬁnancial applications purposes by [6].”
Fractional Processes as Models in Stochastic Finance (2010, methodology): “Indeed, in [13] it is shown that in this case the mixed fBm is actually equivalent in law to a Bm.”
Fractional Brownian motion (2006, result): “Let us mention the following surprising result proved by Cheridito in [8].”
Pricing Currency Option in a Mixed Fractional Brownian Motion with Jumps Environment (2014, background): “Now we list some properties in [52, 54] by the following propositions.”