Improved Predictor Corrector Scheme for Solving Cox-Inegrsoll-Ross Interest Rate Model: A Comprehensive Analysis and Applications in Financial Modeling
Abstract
An Uncertain Differential Equation (UDE) is a type of differential equation driven by Liu’s canonical process. It has always been a tough problem to obtain the analytic solution of UDE. In this paper, we study a new numerical method for solving UDEs: the Improved Predictor-Corrector (IPC). Also, we translate a UDE into a system of ODEs using the concept of an α-path, which is a certain type of function. Moreover, the convergence and stability of the IPC method are detailed. This method has many applications in Financial mathematics from a numerical perspective. Furthermore, this research comprehensively analyzes the Cox-Ingersoll-Ross (CIR) interest rate model and explores its application in financial modeling. The CIR model is widely used in finance to model interest rates and has proven to be a valuable tool for understanding and predicting interest rate dynamics. Through comprehensive analysis and exploration of the interest rate model, the CIR aims to deepen understanding of interest rates, examine its application across various financial contexts, and provide deeper insight into the crucial role of interest rates in effective financial decision-making. Finally, we present various examples to show our assertions.
Keywords:
Fuzzy canonical Liu’s process, Improved predictor corrector method, Cox Ingersoll-Ross modelReferences
- [1] Liu, G. (2025). Uncertainty theory. AI & society, 1–12. https://doi.org/10.1007/s00146-025-02532-2
- [2] Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of uncertain systems, 2(1), 3–16. https://jus.worldscientific.com/pdf/jusVol02No1paper01.pdf
- [3] Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and systems: An international journal, 41(7), 535–547. https://doi.org/10.1080/01969722.2010.511552
- [4] Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy optimization and decision making, 9(1), 69–81. https://doi.org/10.1007/s10700-010-9073-2
- [5] Yao, K., Gao, J., & Gao, Y. (2013). Some stability theorems of uncertain differential equation. Fuzzy optimization and decision making, 12(1), 3–13. https://doi.org/10.1007/s10700-012-9139-4
- [6] Chen, X., & Qin, Z. (2011). A new existence and uniqueness theorem for fuzzy differential equations. International journal of fuzzy systems, 13(2), p148. https://openurl.ebsco.com/EPDB%3Agcd%3A1%3A15347041/detailv2?sid=ebsco%3Aplink%3Ascholar&id=ebsco%3Agcd%3A67677662&crl=c&link_origin=scholar.google.com
- [7] Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of intelligent & fuzzy systems, 25(3), 825–832. https://doi.org/10.3233/IFS-120688
- [8] Yang, X., & Shen, Y. (2015). Runge-Kutta method for solving uncertain differential equations. Journal of uncertainty analysis and applications, 3(1), 17. https://doi.org/10.3233/IFS-120688
- [9] Yang, X., & Ralescu, D. A. (2015). Adams method for solving uncertain differential equations. Applied mathematics and computation, 270, 993–1003. https://doi.org/10.1016/j.amc.2015.08.109
- [10] Wang, X., Ning, Y., Moughal, T. A., & Chen, X. (2015). Adams--Simpson method for solving uncertain differential equation. Applied mathematics and computation, 271, 209–219. https://doi.org/10.1016/j.amc.2015.09.009
- [11] Liu, B. (2009). Some research problems in uncertainty theory. Journal of uncertain systems, 3(1), 3–10. https://jus.worldscientific.com/pdf/jusVol03No1paper01.pdf
- [12] Gao, Y. (2012). Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition. Journal of uncertain systems, 6(3), 223–232. https://jus.worldscientific.com/pdf/jusVol06No3paper05.pdf
Issue 1