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

Runhuan Feng ()
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Runhuan Feng: University of Illinois at Urbana-Champaign

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 691-715

Abstract: Abstract 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.

Keywords: Stochastic integral representation; Martingale representation; Itô formula; Time-homogeneous diffusion processes; Running extremum; Primary 60J60; Secondary 60G17 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9467-2

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