In this article, we study a class of stochastic differential equations driven by a fractional
Brownian motion with H> 1/2 and a discontinuous coefficient in the diffusion. We prove …

We give several extensions of the sewing lemma of Feyel and de La Pradelle and show how
these results generalize Young's integration theory in a simple and natural way. For …

We investigate Wiener-transformable markets, where the driving process is given by an
adapted transformation of a Wiener process. This includes processes with long memory, like …

We study integral representations of random variables with respect to general Hölder
continuous processes and with respect to two particular cases; fractional Brownian motion …

We show that small ball estimates together with Hölder continuity assumption allow to obtain
new representation results in models with long memory. In order to apply these results, we …

Full article: Integral Representation with Adapted Continuous Integrand with Respect to
Fractional Brownian Motion Skip to Main Content Taylor and Francis Online homepage Taylor …

It was shown in Mishura et al.(Stochastic Process. Appl. 123 (2013) 2353–2369), that any
random variable can be represented as improper pathwise integral with respect to fractional …

We show that if a random variable is the final value of an adapted log-Hölder continuous
process, then it can be represented as a stochastic integral with respect to a fractional …

We review the use of fractional Brownian motion in financial modeling with an emphasis on
arbitrage and hedging in the (mixed) fractional Black–Scholes model for stock prices …

This paper deals with stochastic integrals of form $\int_0^ T f (X_u) d Y_u $ in a case where
the function $ f $ has discontinuities, and hence the process $ f (X) $ is usually of …