Dynamic Mean-Variance Optimisation Problems with Deterministic Information

30 Pages Posted: 12 Oct 2017 Last revised: 23 Feb 2018

See all articles by Martin Schweizer

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Danijel Zivoi

ETH Zürich

Mario Sikic

University of Zurich

Date Written: September 29, 2017

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.

Keywords: Mean-Variance Hedging, Mean-Variance Portfolio Selection, Restricted Information, Partial Information, Deterministic Strategies, Quadratic Optimisation Problems, Nancial Markets, Type (A) Semimartingales

JEL Classification: G11, G13, C61, C60

Suggested Citation

Schweizer, Martin and Zivoi, Danijel and Sikic, Mario, Dynamic Mean-Variance Optimisation Problems with Deterministic Information (September 29, 2017). Swiss Finance Institute Research Paper No. 17-29, Available at SSRN: https://ssrn.com/abstract=3051199 or http://dx.doi.org/10.2139/ssrn.3051199

Martin Schweizer (Contact Author)

ETH Zurich ( email )

Mathematik, HG G51.2
Raemistrasse 101
CH-8092 Zurich
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Danijel Zivoi

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Mario Sikic

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

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