Existence Theorem for Mean-Reverting CEV Process with Regime Switching

DOI

10.2991/meic-15.2015.357How to use a DOI?

Keywords

CEV process; global solution; Gronwall's inequality; Lipschitz condition; regime switching

Abstract

Empirical studies show that the most successful continuous-time models of the short term rate in capturing the dynamics are those that allow the volatility of interest changes to be highly sensitive to the level of the rate. The mean-reverting constant elasticity of variance (CEV) process with regime switching is a stochastic differential equation that has found considerable use as a model for interest rate, volatility, and other financial quantities. Since the coefficients of CEV process do not satisfy the linear growth condition, we can not examine its properties by traditional techniques. This paper overcomes the mathematical difficulties due to the nonlinear growth of the mean-reverting CEV process with regime switching, and provides a detailed proof that there is a unique positive global solution for such SDE.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Ruxing Xu
AU  - Dan Wu
AU  - Ronghua Yi
PY  - 2015/04
DA  - 2015/04
TI  - Existence Theorem for Mean-Reverting CEV Process with Regime Switching
BT  - Proceedings of the 2015 International Conference on Mechatronics, Electronic, Industrial and Control Engineering
PB  - Atlantis Press
SP  - 1560
EP  - 1563
SN  - 2352-5401
UR  - https://doi.org/10.2991/meic-15.2015.357
DO  - 10.2991/meic-15.2015.357
ID  - Xu2015/04
ER  -