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Backward Stochastic PDE and Imperfect Hedging

Author

Listed:
  • M. Mania

    (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St., Tbilisi 0193, Georgia)

  • R. Tevzadze

    (Institute of Cybernetics, Georgian Academy of Sciences, 5, S. Euli St., Tbilisi 0186, Georgia)

Abstract

We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by anRd-valued continuous semimartingale. Under some regularity assumptions we derive a backward stochastic PDE for the value function of the problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As an example the case of mean-variance hedging is considered.

Suggested Citation

  • M. Mania & R. Tevzadze, 2003. "Backward Stochastic PDE and Imperfect Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 663-692.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:07:n:s0219024903002122
    DOI: 10.1142/S0219024903002122
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    References listed on IDEAS

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    1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    6. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
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