Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching

Zhenzhong Zhang; Enhua Zhang; Jinying Tong

doi:10.3934/dcdsb.2018053

Article Contents

2018, Volume 23, Issue 6: 2433-2455. Doi: 10.3934/dcdsb.2018053

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Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching

Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Author Bio: zzzhang@dhu.edu.cn(ZhenzhongZhang); enhuazhang1993@163.com(EnhuaZhang); jytong@dhu.edu.cn(JinyingTong)
* Corresponding author: Jinying Tong.
* Corresponding author: Jinying Tong.

Received: April 2017

Revised: September 2017

Early access: February 2018

Published: June 2018

The author Zhenzhong Zhang is supported by the Humanities and Social Sciences Fund of Ministry of Education of China (No. 17YJA910004). The author Jinying Tong is supported by the National Natural Science Foundation of China (Nos. 11401093 and 11471071).

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Abstract

In this paper, we consider long time behavior of the Cox-Ingersoll-Ross (CIR) interest rate model driven by stable processes with Markov switching. Under some assumptions, we prove an ergodicity-transience dichotomy, namely, the interest rate process is either ergodic or transient. The sufficient and necessary conditions for ergodicity and transience of such interest model are given under some assumptions. Finally, an application to interval estimation of the interest rate processes is presented to illustrate our results.

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Mathematics Subject Classification: Primary: 60G52, 60J27.

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Figure 1. Computer simulation of a single path of $X_t$ with initial value $X_0 = 0.3,r_0 = 1$ and different coefficients $\alpha = 1.25$(up), $\alpha = 1.75$(down)

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Figure 2. Computer simulation of a single path of $X_t$ with initial value $X_0 = 0.3,r_0 = 1$ and $\alpha = 1.75$.

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