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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Volume 26, Issue 1


Comparison results for path-dependent options

Jan Bergenthum / Ludger Rüschendorf
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.2008.0912


In this paper comparison results of convex type are established for several path-dependent options in some classes of semimartingale models. The options considered are some classes of lookback options, Asian and American options and barrier options. Comparison of the path-dependent options is based on ordering properties of the local characteristics of the underlying processes as well as on suitable propagation of convexity property. These properties allow a stochastic analysis of the basic linking process which establishes a link between the value processes in the underlying models. The linking process gives a unified tool to obtain comparison results for these path-dependent options. This paper extends and unifies several results in the literature.

Keywords: path dependent options; lookback option; convex order; Levy process; semimartingale

About the article

* Correspondence address: University of Freiburg, Department of Mathematics, Eckerstraße 1, 79104 Freiburg, Deutschland,

Published Online: 2009-09-25

Published in Print: 2008-03-01

Citation Information: Statistics & Decisions International mathematical journal for stochastic methods and models, Volume 26, Issue 1, Pages 53–72, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2008.0912.

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