Moments and ergodicity of the jump-diffusion CIR process

ABSTRACT

We study the jump-diffusion CIR process, which is an extension of the Cox-Ingersoll-Ross model and whose jumps are introduced by a subordinator. We provide sufficient conditions on the Lévy measure of the subordinator under which the jump-diffusion CIR process is ergodic and exponentially ergodic, respectively. Furthermore, we characterize the existence of the κ-moment ($\kappa >0$) of the jump-diffusion CIR process by an integrability condition on the Lévy measure of the subordinator.

KEYWORDS:

• CIR model with jumps
• ergodicity
• exponential ergodicity
• Forster-Lyapunov function
• fractional moment

AMS SUBJECT CLASSIFICATIONS:

• Primary 60J25
• 37A25
• Secondary 60J35
• 60J75

Acknowledgements

We are very grateful to the anonymous referees, whose valuable comments have led to an improvement of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.