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Research Article | Open Access

Existence results for the Cox–Ingersoll–Ross model with variable exponent diffusion

Faculty of Science and Technology, Applied Mathematics, Athabasca University, Athabasca, AB, T9S3A3, Canada
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Abstract

This study proposes a new stochastic model where the diffusion coefficient involves a state-dependent variable exponent function p ( ⋅ ). This new theoretically flexible framework generalizes the classical Cox–Ingersoll–Ross model. The existence, uniqueness, and higher moment properties of solutions are analyzed. The validity and efficiency of the model is illustrated with numerical experiments. Finally, a detailed analysis for Itô vs. Stratonovich interpretations of the proposed model is provided.

Keywords

stochastic processstate-dependent variable exponentCox-Ingersoll-Ross (CIR) modeltruncation procedurePicard iterationsnon-Lipschitz diffusion coefficientmoment estimates
CLC number: 60G07, 60H15, 60H20, 60H30

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 22106-22126
DOI: 10.3934/math.2025984

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Avci M. Existence results for the Cox–Ingersoll–Ross model with variable exponent diffusion. AIMS Mathematics, 2025, 10(9): 22106-22126. https://doi.org/10.3934/math.2025984

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Received: 05 July 2025
Revised: 08 September 2025
Accepted: 18 September 2025
Published: 23 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)