December 2012 Convex duality in mean-variance hedging under convex trading constraints
Christoph Czichowsky, Martin Schweizer
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Adv. in Appl. Probab. 44(4): 1084-1112 (December 2012). DOI: 10.1239/aap/1354716590


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.


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Christoph Czichowsky. Martin Schweizer. "Convex duality in mean-variance hedging under convex trading constraints." Adv. in Appl. Probab. 44 (4) 1084 - 1112, December 2012.


Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1277.60079
MathSciNet: MR3052850
Digital Object Identifier: 10.1239/aap/1354716590

Primary: 49N10 , 60G48 , 91G10 , 93E20
Secondary: 60H05

Keywords: constraints , convex duality , Mean-variance hedging , stochastic integral

Rights: Copyright © 2012 Applied Probability Trust


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Vol.44 • No. 4 • December 2012
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