An information geometry problem in mathematical finance

I. Csiszár, Thomas Breuer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Familiar approaches to risk and preferences involve minimizing the expectation EIP(X) of a payoff function X over a family Γ of plausible risk factor distributions IP. We consider Γ determined by a bound on a convex integral functional of the density of IP, thus Γ may be an I-divergence (relative entropy) ball or some other f-divergence ball or Bregman distance ball around a default distribution IP0. Using a Pythagorean identity we show that whether or not a worst case distribution exists (minimizing EIP(X) subject to IP ∈ Γ), the almost worst case distributions cluster around an explicitly specified, perhaps incomplete distribution. When Γ is an f-divergence ball, a worst case distribution either exists for any radius, or it does/does not exist for radius less/larger than a critical value. It remains open how far the latter result extends beyond f-divergence balls.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages435-443
Number of pages9
Volume9389
ISBN (Print)9783319250397, 9783319250397
DOIs
Publication statusPublished - 2015
Event2nd International Conference on Geometric Science of Information, GSI 2015 - Palaiseau, France
Duration: Oct 28 2015Oct 30 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9389
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2nd International Conference on Geometric Science of Information, GSI 2015
CountryFrance
CityPalaiseau
Period10/28/1510/30/15

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Keywords

  • Almost worst case densities
  • Bregman distance
  • Convex integral functional
  • Fdivergence
  • I-divergence
  • Payoff function
  • Pythagorean identity
  • Risk measure
  • Worst case density

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Csiszár, I., & Breuer, T. (2015). An information geometry problem in mathematical finance. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 435-443). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9389). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_47