Lie Symmetries, Optimal System, and Invariant Solutions of the Generalized Cox-Ingersoll-Ross Equation

DOI

10.2991/978-94-6463-014-5_11How to use a DOI?

Keywords

Cox-Ingersoll-Ross (CIR) model; Lie symmetry analysis; Optimal system; invariant solutions

Abstract

The Cox-Ingersoll-Ross (CIR) model is a short-rate model and is widely used in the finance field to predict the movement of interest rates in bond pricing models. This paper exploited Lie symmetry analysis to solve the generalized CIR model by determining the infinitesimal generators. Lie symmetry is one of the powerful tools to solve the partial differential equation (PDE) analytically by reducing the PDE into a lower form. Besides, an optimal system of one-dimensional subalgebras is constructed and then used to reduce the generalized CIR equation by introducing the similarity variables. Lastly, the invariant solutions are obtained by solving the reduced equation.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - H. S. Tang
AU  - K. Y. Chong
AU  - B. H. Kee
PY  - 2022
DA  - 2022/12/12
TI  - Lie Symmetries, Optimal System, and Invariant Solutions of the  Generalized Cox-Ingersoll-Ross Equation
BT  - Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022)
PB  - Atlantis Press
SP  - 103
EP  - 113
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-014-5_11
DO  - 10.2991/978-94-6463-014-5_11
ID  - Tang2022
ER  -