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Comparing Brownian Stochastic Integrals for the Convex Order

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Modern Stochastics and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 90))

Abstract

We show that, in general, inequalities between integrands with respect to Brownian motion do not lead to majorization in the convex order for the corresponding stochastic integrals. Particular examples and counterexamples are discussed.

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Author information

Authors and Affiliations

  1. Laboratoire d’Analyse et Probabilités, Université d’Évry-Val d’Essonne, 23 Boulevard de France, F-91037, Evry Cedex, France

    Francis Hirsch

  2. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 Place Jussieu, Case 188, F-75252, Paris Cedex 05, France

    Marc Yor

  3. Institut Universitaire de France, Paris, France

    Marc Yor

Authors
  1. Francis Hirsch
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  2. Marc Yor
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Corresponding author

Correspondence to Marc Yor .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Volodymyr Korolyuk

  2. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, Compiegne Cedex, France

    Nikolaos Limnios

  3. Dept. of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuliya Mishura

  4. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Lyudmyla Sakhno

  5. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Georgiy Shevchenko

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Hirsch, F., Yor, M. (2014). Comparing Brownian Stochastic Integrals for the Convex Order. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_1

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