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On-line trading as a renewal process: Waiting time and inspection paradox

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  • Jun-ichi Inoue
  • Naoya Sazuka
  • Enrico Scalas

Abstract

We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. The basic method of our approach depends on the so-called renewal-reward theorem. Assuming that the stochastic process modelling the price change is a renewal process, we use the theorem to calculate the average waiting time of the process. The so-called ``inspection paradox'' is discussed, which, in general, means that the average durations is shorter than the average waiting time.

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  • Jun-ichi Inoue & Naoya Sazuka & Enrico Scalas, 2010. "On-line trading as a renewal process: Waiting time and inspection paradox," Papers 1007.3347, arXiv.org.
    • Handle: RePEc:arx:papers:1007.3347
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    Cited by:

    1. Bertram During & Nicos Georgiou & Enrico Scalas, 2016. "A stylized model for wealth distribution," Papers 1609.08978, arXiv.org, revised Jul 2021.
    2. Takero Ibuki & Jun-ichi Inoue, 2011. "Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 6(2), pages 93-120, November.

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