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A stochastic model for speculative bubbles

Author

Listed:
  • S'ebastien Gadat
  • Laurent Miclo
  • Fabien Panloup

Abstract

This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order Markov process, which after simple transformations can be viewed as a turning two-dimensional Gaussian process. Then, our main problem is to ob- tain some bounds for the persistence rate relative to the return time to a given price. In our main results, we prove with both spectral and probabilistic methods that this rate is almost proportional to the turning frequency {\omega} of the model and provide some explicit bounds. In the continuity of this result, we build some estimators of {\omega} and of the pseudo-period of the prices. At last, we end the paper by a proof of the quasi-stationary distribution of the process, as well as the existence of its persistence rate.

Suggested Citation

  • S'ebastien Gadat & Laurent Miclo & Fabien Panloup, 2013. "A stochastic model for speculative bubbles," Papers 1309.6287, arXiv.org.
  • Handle: RePEc:arx:papers:1309.6287
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    References listed on IDEAS

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    1. Ben S. Bernanke & Mark Gertler, 2001. "Should Central Banks Respond to Movements in Asset Prices?," American Economic Review, American Economic Association, vol. 91(2), pages 253-257, May.
    2. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    3. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-1181, September.
    4. Emmanuel Farhi & Jean Tirole, 2012. "Bubbly Liquidity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 678-706.
    5. Alexander Kiselev & Lenya Ryzhik, 2010. "A simple model for asset price bubble formation and collapse," Papers 1009.0299, arXiv.org.
    6. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Gadat, Sébastien & Panloup, Fabien & Saadane, Sofiane, 2016. "Stochastic Heavy Ball," TSE Working Papers 16-712, Toulouse School of Economics (TSE).

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