A Stochastic Model for the Variation of Fourier Series Expansions with Time Delay Arising in Financial Market Price Changes

  • I. U. Amadi Department of Mathematics Statistics, Captain Elechi Amadi Polytechnics, Port Harcourt, Nigeria
  • C. P. N. Ogbogbo Department of Mathematics, University of Ghana, Legon. Accra, Ghana.
  • I. Davies Department of Mathematics, Rivers State University Orowurukwo, Port Harcourt, Nigeria.
  • T. Katsekpor Department of Mathematics, University of Ghana, Legon. Accra, Ghana.
Keywords: Asset Pricing, Return rates, Fourier series expansions, Stochastic Analysis, Time Delay

Abstract

In this paper, we derive a closed-form solution for the Stochastic Delay Differential Equation
(SDDE). We formulated and proved theorems using Fourier series coefficients, which provided
exact conditions for asset proce returns in three scenarios : linear, quadratic, and cubic functions.
These price functions were utilized as the drift, representing the return rate in the SDDE
solution, resulting in three distinct solutions. We empirically evaluated these solutions to analyze the periodic impact of delay on each asset price
function, revealing that an increase in the delay parameter reduces the value of time-varying
asset investments. Finally, our comparison of the asset values indicated that return rates following a linear trend
offer the highest precision.

Published
2024-07-30
How to Cite
Amadi, I. U., Ogbogbo, C. P. N., Davies, I., & Katsekpor, T. (2024). A Stochastic Model for the Variation of Fourier Series Expansions with Time Delay Arising in Financial Market Price Changes. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), 140 - 153. Retrieved from http://ijmso.unilag.edu.ng/article/view/2237
Issue
Vol 10 No 3 (2024)
Section
Articles

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