DYNAMIC MEAN–VARIANCE OPTIMIZATION PROBLEMS WITH DETERMINISTIC INFORMATION

Martin Schweizer, Danijel Zivoi () and Mario Šikić ()
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Martin Schweizer: ETH Zürich, Mathematik, HG G51.2, Rämistrasse 101, CH 8092 Zürich, Switzerland2Swiss Finance Institute, Walchestrasse 9, CH 8006 Zürich, Switzerland
Danijel Zivoi: ETH Zürich, Mathematik, HG GO47.2, Rämistrasse 101, CH 8092 Zürich, Switzerland
Mario Šikić: Universität Zürich, Center for Finance and Insurance, AND 2.41, Andreasstrasse 15, CH 8050 Zürich, Switzerland

International Journal of Theoretical and Applied Finance (IJTAF), 2018, vol. 21, issue 02, 1-38

Abstract: 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 S is a semimartingale, but not adapted to the filtration 𝔾 which models the information available for constructing trading strategies. We choose as 𝔾 = 𝔽det the zero-information filtration and assume that S 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.

Keywords: Mean–variance hedging; mean–variance portfolio selection; restricted information; partial information; deterministic strategies; quadratic optimization problems; financial markets; type (A) semimartingales (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024918500115

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