Stochastic processes are widely used for model building in the social, physical, engineering
and life sciences as well as in financial economics. In model building, statistical inference for …

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena
in diverse fields from biology to finance. This huge range of potential applications makes …

This volume examines the theory of fractional Brownian motion and other long-memory
processes. Interesting topics for PhD students and specialists in probability theory …

The price variation of the correlated fractal transmission system is used to deduce the
fractional Black–Scholes model that has an α α-order time fractional derivative. The …

We establish a simple no‐arbitrage criterion that reduces the absence of arbitrage
opportunities under proportional transaction costs to the condition that the asset price …

This work deals with the put option pricing problems based on the time‐fractional Black‐
Scholes equation, where the fractional derivative is a so‐called modified Riemann‐Liouville …

In this paper, we present a numerical technique for solving the time-fractional Black-Scholes
(TFBS) equation describing European options. The time-fractional derivative is described by …

To price vanilla European and American options via the fractional Black–Scholes model, first
a (2− α)-order discretization scheme for the Caputo fractional derivative based upon graded …

In the second part of the past decade, the usage of fractional Brownian motion for financial
models was stuck. The favorable time-series properties of fractional Brownian motion …

The mathematical modeling in trade and finance issues is the key purpose in the
computation of the value and considering option during preferences in contract. This paper …