Stochastic Integral Representations of the Extrema of Time-homogeneous Diffusion Processes

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The stochastic integral representations (martingale representations) of square integrable processes are well-studied problems in applied probability with broad applications in finance. Yet finding explicit expression is not easy and typically done through the Clack-Ocone formula with the advanced machinery of Malliavin calculus. To find an alternative, Shiryaev and Yor (Teor Veroyatnost i Primenen 48(2):375–385, 2003) introduced a relatively simple method using Itô’s formula to develop representations for extrema of Brownian motion. In this paper, we extend their work to provide representations of functionals of time-homogeneous diffusion processes based on the Itô’s formula.

Original languageEnglish (US)
Pages (from-to)691-715
Number of pages25
JournalMethodology and Computing in Applied Probability
Issue number3
StatePublished - Sep 1 2016


  • Itô formula
  • Martingale representation
  • Running extremum
  • Stochastic integral representation
  • Time-homogeneous diffusion processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)


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