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Sequential maximum likelihood estimation for reflected generalized Ornstein–Uhlenbeck processes

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  • Bo, Lijun
  • Yang, Xuewei

Abstract

In this paper, we investigate a sequential maximum likelihood estimator of the unknown drift parameter for a class of reflected generalized Ornstein–Uhlenbeck processes driven by spectrally positive Lévy processes. In both of the cases of negative drift and positive drift, we prove that the sequential maximum likelihood estimator of the drift parameter is closed, unbiased, normally distributed and strongly consistent. Finally a numerical test is presented to illustrate the efficiency of the estimator.

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  • Bo, Lijun & Yang, Xuewei, 2012. "Sequential maximum likelihood estimation for reflected generalized Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1374-1382.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1374-1382
    DOI: 10.1016/j.spl.2012.03.018
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    References listed on IDEAS

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    1. Lijun Bo & Yongjin Wang & Xuewei Yang, 2010. "Some integral functionals of reflected SDEs and their applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 343-348.
    2. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    3. Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 280-291.
    4. Lépingle, D., 1995. "Euler scheme for reflected stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 119-126.
    5. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
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    Cited by:

    1. Huantian Xie & Nenghui Kuang, 2021. "Sequential Maximum Likelihood Estimation for the Squared Radial Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1409-1417, December.
    2. Qingpei Zang & Lixin Zhang, 2019. "Asymptotic Behaviour of the Trajectory Fitting Estimator for Reflected Ornstein–Uhlenbeck Processes," Journal of Theoretical Probability, Springer, vol. 32(1), pages 183-201, March.

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