### Convex duality in mean-variance hedging under convex trading constraints

#### 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.

#### Article information

Source
Adv. in Appl. Probab., Volume 44, Number 4 (2012), 1084-1112.

Dates
First available in Project Euclid: 5 December 2012

https://projecteuclid.org/euclid.aap/1354716590

Digital Object Identifier
doi:10.1239/aap/1354716590

Mathematical Reviews number (MathSciNet)
MR3052850

Zentralblatt MATH identifier
1277.60079

#### Citation

Czichowsky, Christoph; Schweizer, Martin. Convex duality in mean-variance hedging under convex trading constraints. Adv. in Appl. Probab. 44 (2012), no. 4, 1084--1112. doi:10.1239/aap/1354716590. https://projecteuclid.org/euclid.aap/1354716590

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