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-Ingersol-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.