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Convex duality in mean-variance hedging under convex trading constraints

Czichowsky, Christoph and Schweizer, Martin (2012) Convex duality in mean-variance hedging under convex trading constraints. Advances in Applied Probability, 44 (4). pp. 1084-1112. ISSN 0001-8678

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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.

Item Type: Article
Official URL:
Additional Information: © 2012 Applied Probability Trust
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 01 Oct 2013 07:46
Last Modified: 16 May 2024 01:31

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