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Convex Duality in Mean Variance Hedging Under Convex Trading Constraints

Author

Listed:
  • Christoph Czichowsky

    (Vienna University of Technology)

  • Martin Schweizer

    (ETH Zürich)

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.

Suggested Citation

  • Christoph Czichowsky & Martin Schweizer, 2012. "Convex Duality in Mean Variance Hedging Under Convex Trading Constraints," Swiss Finance Institute Research Paper Series 12-24, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1224
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    Cited by:

    1. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    2. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.

    More about this item

    Keywords

    mean-variance hedging; constraints; stochastic integrals; convex duality;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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