Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market

Ting Jin and Xiangfeng Yang

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 203-221

Abstract: Uncertain fractional differential equations (UFDEs) have non-locality features to reflect memory and hereditary characteristics for the asset price changes, thus are more suitable to model the real financial market. Based on this characteristic, this paper primarily investigates the monotonicity theorem for uncertain fractional differential equations in Caputo sense and its application. Firstly, monotonicity theorems for solutions of UFDEs are presented by using the α-path method. Secondly, as the application of the monotone function theorem, a novel uncertain fractional mean-reverting model with a floating interest rate is presented. Lastly, the pricing formulas of the European and American options are derived for the proposed model based on the monotone function and present extreme values and time integral theorems, respectively. In addition, numerical schemes are designed, and numerical calculations are illustrated concerning different parameters through the predictor–corrector method.

Keywords: Fractional differential equation; Uncertainty distribution; Predictor–corrector method; Option price; α-path (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421001890
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:203-221

DOI: 10.1016/j.matcom.2021.05.018

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().