On predicting the ultimate maximum for exponential Lévy processes

Katsunori Ano, Roman V. Ivanov

研究成果: Article査読

5 被引用数 (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].

ジャーナルElectronic Communications in Probability
出版ステータスPublished - 2012

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性


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