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AN ASYMPTOTIC THEORY FOR JUMP DIFFUSION MODELS

Published online by Cambridge University Press:  02 April 2024

Minsoo Jeong  and
Joon Y. Park
Minsoo Jeong
Affiliation:
Yonsei University
Joon Y. Park*
Affiliation:
Indiana University
*
Address correspondence to Joon Y. Park, Department of Economics, Indiana University, Bloomington, IN, United States, joon@indiana.edu
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Abstract

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This paper presents an asymptotic theory for recurrent jump diffusion models with well-defined scale functions. The class of such models is broad, including general nonstationary as well as stationary jump diffusions with state-dependent jump sizes and intensities. The asymptotics for recurrent jump diffusion models with scale functions are largely comparable to the asymptotics for the corresponding diffusion models without jumps. For stationary jump diffusions, our asymptotics yield the usual law of large numbers and the standard central limit theory with normal limit distributions. The asymptotics for nonstationary jump diffusions, on the other hand, are nonstandard and the limit distributions are given as generalized diffusion processes.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 63
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We thank the editor, a co-editor, and two anonymous referees for many useful comments. We are also grateful for helpful discussions with Eric Renault, Yoosoon Chang, Jihyun Kim, Bin Wang, and the seminar participants at Yonsei, Indiana, Yale, Michigan State, Michigan, Queens, Penn State, LSE, and Oxford University. This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019S1A5A8034332).

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