Analysis of fractional differential equation and its application to realistic data

Reem Abdullah Aljethi and Adem Kılıçman

Chaos, Solitons & Fractals, 2023, vol. 171, issue C

Abstract: This paper aims to propose a new a Fractional differential equation which derived from the classical Lévy model by introducing new parameters in order to fit the realistic data. The model is based on a combination of generalized tempered stable (GTS) process and Lévy stable process (LSP). A numerical method is chosen to solve the fractional partial differential equation associated to Fractional Lévy Stochastic model. Then, using the accurate information collected from the Yahoo Finance, the inverse approach is applied to estimate the unknown parameters for the Fractional Lévy stochastic model. Finally, numerical results are presented and a conclusion is drawn.

Keywords: Lévy process; Yahoo finance; Fractional diffusion equations; Optimization methods (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003478

DOI: 10.1016/j.chaos.2023.113446

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