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

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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.

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Authors and Affiliations

  1. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Runhuan Feng

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  1. Runhuan Feng
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Correspondence to Runhuan Feng.

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The authors declare that they have no conflict of interest. This research does not involve human participants or animals.

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Feng, R. Stochastic Integral Representations of the Extrema of Time-homogeneous Diffusion Processes. Methodol Comput Appl Probab 18, 691–715 (2016). https://doi.org/10.1007/s11009-015-9467-2

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  • DOI: https://doi.org/10.1007/s11009-015-9467-2

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