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Mathematics and Financial Economics

, Volume 8, Issue 2, pp 109–134 | Cite as

Local risk-minimization under the benchmark approach

  • Francesca BiaginiEmail author
  • Alessandra Cretarola
  • Eckhard Platen
Article

Abstract

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extremely weak assumptions a much richer modeling world than the classical methodology.

Keywords

Local risk-minimization Föllmer–Schweizer decomposition  Numéraire portfolio Benchmark approach Real world pricing 

JEL Classification

C02 G10 G13 

Notes

Acknowledgments

The authors like to thank Martin Schweizer and Wolfgang Runggaldier for valuable discussions. We also express our gratitude to an unknown referee, whose comments contributed to significant improvements of the presentation of this manuscript. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no [228087].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Francesca Biagini
    • 1
    Email author
  • Alessandra Cretarola
    • 2
  • Eckhard Platen
    • 3
  1. 1.Department of MathematicsLMUMunichGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of PerugiaPerugiaItaly
  3. 3.Finance Discipline Group, Department of Mathematical SciencesUniversity of Technology SydneyBroadwayAustralia

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