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

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  • Runhuan Feng

    (University of Illinois at Urbana-Champaign)

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.

Suggested Citation

  • Runhuan Feng, 2016. "Stochastic Integral Representations of the Extrema of Time-homogeneous Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 691-715, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9467-2
    DOI: 10.1007/s11009-015-9467-2
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    References listed on IDEAS

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    1. Ning Cai & Chenxu Li & Chao Shi, 2014. "Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 789-822, August.
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    3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
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