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Large time and small noise asymptotic results for mean reverting diffusion processes with applications

Author

Listed:
  • Jeffrey Callen

    (Stern School of Business, New York University, New York, NY 10012, USA)

  • Lin Xu

    (School of Engineering, Princeton University, New Jersey, NJ 08554, USA)

  • Suresh Govindaraj

    (Graduate School of Business, Columbia University, New York, NY 10027, USA)

Abstract

We use the theory of large deviations to investigate the large time behavior and the small noise asymptotics of random economic processes whose evolutions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show that the probability is exponentially small that the time averages of these process will occupy regions distinct from their stable equilibrium position. We also demonstrate that as the noise parameter decreases, there is an exponential convergence to the stable position. Applications of large deviation techniques and public policy implications of our results for regulators are explored.

Suggested Citation

  • Jeffrey Callen & Lin Xu & Suresh Govindaraj, 2000. "Large time and small noise asymptotic results for mean reverting diffusion processes with applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 401-419.
    • Handle: RePEc:spr:joecth:v:16:y:2000:i:2:p:401-419
    Note: Received: December 7, 1998; revised version: October 25, 1999
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    Citations

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    Cited by:

    1. Edward Lee & Norman Strong & Zhenmei (Judy) Zhu, 2014. "Did Regulation Fair Disclosure, SOX, and Other Analyst Regulations Reduce Security Mispricing?," Journal of Accounting Research, Wiley Blackwell, vol. 52(3), pages 733-774, June.
    2. Govindaraj, Suresh, 2005. "Hypothesis testing for diffusion processes with continuous observations: Direct computation of large deviation results for error probabilities," Finance Research Letters, Elsevier, vol. 2(4), pages 234-247, December.
    3. Katsuhiko Muramiya & Kazuhisa Otogawa & Tomomi Takada, 2008. "Abnormal Accrual, Informed Trader, and Long-Term Stock Return: Evidence from Japan," Discussion Paper Series 233, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    Keywords

    Large deviations; Level-2-large deviations; Exit problems; Mean reverting stochastic differential equations.;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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