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Parameter estimation for generalized diffusion processes with reflected boundary

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Abstract

Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein-Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. In this paper, under certain constraints, we are concerned with the problem of estimating the unknown parameter in the reflected Ornstein-Uhlenbeck processes with the general drift coefficient. The methodology of estimation is built upon the maximum likelihood approach and the method of stochastic integration. The strong consistency and asymptotic normality of estimator are derived. As a by-product of the use, we also establish Girsanov’s theorem of our model in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    QingPei Zang & LiXin Zhang

  2. School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, China

    QingPei Zang

Authors
  1. QingPei Zang
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  2. LiXin Zhang
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Correspondence to QingPei Zang.

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Zang, Q., Zhang, L. Parameter estimation for generalized diffusion processes with reflected boundary. Sci. China Math. 59, 1163–1174 (2016). https://doi.org/10.1007/s11425-015-5112-3

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  • DOI: https://doi.org/10.1007/s11425-015-5112-3

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