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Mean-variance Hedging Under Partial Information

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  • M. Mania
  • R. Tevzadze
  • T. Toronjadze
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    Abstract

    We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that the initial mean variance hedging problem is equivalent to a new mean variance hedging problem with an additional correction term, which is formulated in terms of observable processes. We prove that the value process of the reduced problem is a square trinomial with coefficients satisfying a triangle system of backward stochastic differential equations and the filtered wealth process of the optimal hedging strategy is characterized as a solution of a linear forward equation.

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    File URL: http://arxiv.org/pdf/math/0703424
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    Paper provided by arXiv.org in its series Papers with number math/0703424.

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    Date of creation: Mar 2007
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    Handle: RePEc:arx:papers:math/0703424

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    1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, Springer, vol. 1(3), pages 181-227.
    3. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B, University of Bonn, Germany 209, University of Bonn, Germany.
    4. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(4), pages 385-413.
    5. Martin Schweizer, 1994. "Risk-Minimizing Hedging Strategies Under Restricted Information," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 4(4), pages 327-342.
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