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Optimal partial hedging in a discrete-time market as a knapsack problem

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  • Peter Lindberg

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    Abstract

    We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be treated as so called knapsack problems, which are a widely researched subject in linear programming. This observation gives us better understanding of the problem of optimal hedging in discrete time. Copyright Springer-Verlag 2010

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    File URL: http://hdl.handle.net/10.1007/s00186-010-0327-0
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    Bibliographic Info

    Article provided by Springer in its journal Mathematical Methods of Operations Research.

    Volume (Year): 72 (2010)
    Issue (Month): 3 (December)
    Pages: 433-451

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    Handle: RePEc:spr:compst:v:72:y:2010:i:3:p:433-451

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    Related research

    Keywords: Efficient hedging; Quantile hedging; Knapsack problem; Greedy algorithm; Binomial model;

    References

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    1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    2. Gino Favero, 2001. "Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches," Computational Statistics, Springer, Springer, vol. 53(3), pages 493-503, July.
    3. Martello, Silvano & Pisinger, David & Toth, Paolo, 2000. "New trends in exact algorithms for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, Elsevier, vol. 123(2), pages 325-332, June.
    4. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    5. Gino Favero & Tiziano Vargiolu, 2006. "Shortfall risk minimising strategies in the binomial model: characterisation and convergence," Computational Statistics, Springer, Springer, vol. 64(2), pages 237-253, October.
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    Cited by:
    1. Peter Lindberg, 2012. "Optimal partial hedging of an American option: shifting the focus to the expiration date," Computational Statistics, Springer, Springer, vol. 75(3), pages 221-243, June.

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