On predicting the ultimate maximum for exponential Lévy processes

Katsunori Ano, Roman V. Ivanov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We consider a problem of predicting of the ultimate maximum of the process over a finite interval of time. Mathematically, this problem relates to a particular optimal stopping problem. In this paper we discuss exponential Lévy processes. As the Lévy processes, we discuss α-stable Lévy processes, 0 < α ≤ 2, and generalized hyperbolic Lévy processes. The method of solution uses the representations of these processes as time-changed Brownian motions with drift. Our results generalize results of papers [10] and [24].

Original languageEnglish
JournalElectronic Communications in Probability
Publication statusPublished - 2012


  • Exponential Lévy process
  • Optimal stopping
  • Predicting
  • Selling of asset
  • Utility function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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