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Asynchronous stochastic price pump

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  • Perepelitsa, Misha
  • Timofeyev, Ilya

Abstract

We propose a model for equity trading in a population of agents where each agent acts to achieve his or her target stock-to-bond ratio, and, as a feedback mechanism, follows a market adaptive strategy. In this model only a fraction of agents participates in buying and selling stock during a trading period, while the rest of the group accepts the newly set price. Using numerical simulations we show that the stochastic process settles on a stationary regime for the returns. The mean return can be greater or less than the return on the bond and it is determined by the parameters of the adaptive mechanism. When the number of interacting agents is fixed, the distribution of the returns follows the log-normal density. In this case, we give an analytic formula for the mean rate of return in terms of the rate of change of agents’ risk levels and confirm the formula by numerical simulations. However, when the number of interacting agents per period is random, the distribution of returns can significantly deviate from the log-normal, especially as the variance of the distribution for the number of interacting agents increases.

Suggested Citation

  • Perepelitsa, Misha & Timofeyev, Ilya, 2019. "Asynchronous stochastic price pump," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 356-364.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:356-364
    DOI: 10.1016/j.physa.2018.10.028
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    Cited by:

    1. Misha Perepelitsa & Ilya Timofeyev, 2022. "Self-sustained price bubbles driven by digital currency innovations and adaptive market behavior," SN Business & Economics, Springer, vol. 2(3), pages 1-15, March.
    2. Misha Perepelitsa, 2021. "Psychological dimension of adaptive trading in cryptocurrency markets," Papers 2109.12166, arXiv.org.
    3. Mikhail Perepelitsa, 2022. "Two Models of Speculative Bubbles Dynamics for Cryptocurrency Prices," Applied Economics and Finance, Redfame publishing, vol. 9(4), pages 3646-3646, November.
    4. Misha Perepelitsa, 2021. "Investing in crypto: speculative bubbles and cyclic stochastic price pumps," Papers 2111.11315, arXiv.org, revised Oct 2022.
    5. Misha Perepelitsa & Ilya Timofeyev, 2020. "Self-sustained price bubbles driven by Bitcoin innovations and adaptive behavior," Papers 2012.14860, arXiv.org.

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