FRACTIONAL STOCHASTIC CALCULUS AND MULTIFRACTIONAL PROCESSES: APPLICATIONS IN FINANCIAL MODELING
Abdulgaffar Muhammad , John Nma Aliu, Elton Ezekiel Mick Micah, Ibitomi Taiwo, Anthony Unyime Abasido and Anthony Kolade Adesugba
Volume 10 Issue 1
Abstract
Fractional Brownian motion and multifractional processes revolutionize stochastic modeling in finance by capturing intricacies like long-range dependence and varying irregularities. The study explores the mathematical foundations, multifractional modeling, and applications of these advanced techniques. Fractional Brownian motion, with non-constant Hurst exponent, introduces properties like self-similarity and non-Markov dynamics. Fractional calculus, involving fractional integration and differentiation, provides a framework for unpacking these complexities. Extending stochastic calculus to fractional Brownian motion requires intricate mathematical formulations in defining stochastic integrals and applying techniques like Itô’s formula. Multifractional processes like multifractional Brownian motion enrich modeling by allowing dynamic adaptation of parameters like the Hurst exponent across different time scales. The applications span option pricing using fractional calculus, risk management leveraging multifractal techniques, and portfolio optimization strategies adapted to multifractional dynamics. Along with theoretical challenges, these innovations shape the frontiers of financial theory. Keywords: Fractional Stochastic Calculus, Multifractional Processes, Financial Modeling, Fractional Brownian Motion, Stochastic Calculus, Option Pricing, Risk Management
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