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

This study proposes a new stochastic model where the diffusion coefficient involves a state-dependent variable exponent function $ p(\cdot) $. 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.