Application of Fractal Processes and Fractional Derivatives in Finance, 2nd Edition
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: 25 November 2024 | Viewed by 2017
Special Issue Editor
Interests: asset pricing models; regime-switching model; volatility derivatives; stochastic volatility models; consumption and investment
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Over the past four decades, fractional calculus has represented a rapidly advancing research area, both in its theory and application in practical problems arising in various fields, such as econophysics and mathematical finance, in which self-similar processes, such as the Brownian motion, the Levy stable process and the fractional Brownian motion, are employed. Brownian motion was firstly introduced and applied in finance by Bachelier (1900).
In 1973, the log-price of a stock was modelled as a Brownian motion named the Black–Scholes–Merton model. The Levy stable processes are widely employed in financial econometrics to model the dynamics of stock, commodity, currency exchange prices, etc. The fractional Brownian motion was introduced by Kolmogorov in 1940 and later by Mandelbrot in 1965, and has been applied in hydrology and climatology as well as finance. The dynamics of the volatility of asset prices have been modelled as a fractional Brownian motion in finance and are called rough volatility models. Its applications in finance engender several novel stochastic analysis problems. Fractional diffusion processes are also applied to model the dynamics of underlying assets. The option price under the fractional diffusion setting induces the fractional partial differential equations involving the fractional derivatives with respect to the time. Some closed-form solutions might be found via transform methods in some applications, and numerical methods to solve fractional partial differential equations are developing.
In this Special Issue, we welcome the submission of original research and review articles exploring fractal processes, fractional derivatives and integration, and their applications in finance. The scope of this Special Issue includes, but is not limited to, the following topics:
- The rough volatility model;
- Fractal processes applied in finance and other fields;
- Fractional differential equations;
- Fractional diffusions;
- Transform methods applied in fractional differential equations;
- Numerical methods for fractional partial differential equations;
- Fractional operators.
Dr. Leung Lung Chan
Guest Editor
Manuscript Submission Information
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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- rough volatility model
- fractal processes applied in finance and other fields
- fractional differential equations
- fractional diffusions
- fractional calculus
- transform methods applied in fractional differential equations
- numerical methods for fractional partial differential equations
- fractional operators
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