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On the non-equilibrium density of geometric mean reversion

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  • Yang, Zhaojun
  • Ewald, Christian-Oliver

Abstract

The geometric mean reversion process X([dot operator]) is well known to play a fundamental role in economic dynamic models. While it is known, at least since Merton (1975), that the equilibrium distribution of geometric mean reversion, i.e. the distribution of X([infinity]), is a gamma distribution, an explicit expression for the non-equilibrium distribution, i.e. the distribution of X(t) for t

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  • Yang, Zhaojun & Ewald, Christian-Oliver, 2010. "On the non-equilibrium density of geometric mean reversion," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 608-611, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:608-611
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    References listed on IDEAS

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    1. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 97-123, August.
    2. Christian-Oliver Ewald & Aihua Zhang, 2006. "A new technique for calibrating stochastic volatility models: the Malliavin gradient method," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 147-158.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. Metcalf, Gilbert E. & Hassett, Kevin A., 1995. "Investment under alternative return assumptions Comparing random walks and mean reversion," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1471-1488, November.
    5. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
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    1. R. S. Tunaru, 2018. "Dividend derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 63-81, January.
    2. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.

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