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DYNAMIC MEAN–VARIANCE OPTIMIZATION PROBLEMS WITH DETERMINISTIC INFORMATION
Journal article

DYNAMIC MEAN–VARIANCE OPTIMIZATION PROBLEMS WITH DETERMINISTIC INFORMATION

  • SCHWEIZER, MARTIN Swiss Finance Institute, Walchestrasse 9, CH 8006 Zürich, Switzerland
  • ZIVOI, DANIJEL ETH Zürich, Mathematik, HG GO47.2, Rämistrasse 101, CH 8092 Zürich, Switzerland
  • ŠIKIĆ, MARIO Universität Zürich, Center for Finance and Insurance, AND 2.41, Andreasstrasse 15, CH 8050 Zürich, Switzerland
  • 2018-4-10
Published in:
  • International Journal of Theoretical and Applied Finance. - World Scientific Pub Co Pte Lt. - 2018, vol. 21, no. 02, p. 1850011
English We solve the problems of mean–variance hedging (MVH) and mean–variance portfolio selection (MVPS) under restricted information. We work in a setting where the underlying price process [Formula: see text] is a semimartingale, but not adapted to the filtration [Formula: see text] which models the information available for constructing trading strategies. We choose as [Formula: see text] the zero-information filtration and assume that [Formula: see text] is a time-dependent affine transformation of a square-integrable martingale. This class of processes includes in particular arithmetic and exponential Lévy models with suitable integrability. We give explicit solutions to the MVH and MVPS problems in this setting, and we show for the Lévy case how they can be expressed in terms of the Lévy triplet. Explicit formulas are obtained for hedging European call options in the Bachelier and Black–Scholes models.
Language
  • English
Open access status
closed
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Persistent URL
https://sonar.ch/global/documents/31013
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