Convex Duality in Mean Variance Hedging Under Convex Trading Constraints

37 Pages Posted: 16 Jun 2012 Last revised: 19 Jun 2012

See all articles by Christoph Czichowsky

Christoph Czichowsky

Vienna University of Technology

Martin Schweizer

ETH Zurich; Swiss Finance Institute

Date Written: June 4, 2012

Abstract

We study mean-variance hedging under portfolio constraints in a general semimartingale model. The constraints are formulated via predictable correspondences, meaning that the trading strategy is restricted to lie in a closed convex set which may depend on the state and time in a predictable way. To obtain the existence of a solution, we first establish the closedness in L2 of the space of all gains from trade (i.e., the terminal values of stochastic integrals with respect to the price process of the underlying assets). This is a first main contribution which enables us to tackle the problem in a systematic and unified way. In addition, using the closedness allows us to explain and generalise in a systematic way the convex duality results obtained previously by other authors via ad hoc methods in specific frameworks.

Keywords: mean-variance hedging, constraints, stochastic integrals, convex duality

JEL Classification: C60, G10, G11

Suggested Citation

Czichowsky, Christoph and Schweizer, Martin, Convex Duality in Mean Variance Hedging Under Convex Trading Constraints (June 4, 2012). Swiss Finance Institute Research Paper No. 12-24, Available at SSRN: https://ssrn.com/abstract=2083051 or http://dx.doi.org/10.2139/ssrn.2083051

Christoph Czichowsky

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

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

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