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Dynamic hedging of conditional value-at-risk

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  • Melnikov, Alexander
  • Smirnov, Ivan
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    Abstract

    In this paper, the problem of partial hedging is studied by constructing hedging strategies that minimize conditional value-at-risk (CVaR) of the portfolio. Two dual versions of the problem are considered: minimization of CVaR with the initial wealth bounded from above, and minimization of hedging costs subject to a CVaR constraint. The Neyman–Pearson lemma approach is used to deduce semi-explicit solutions. Our results are illustrated by constructing CVaR-efficient hedging strategies for a call option in the Black–Scholes model and also for an embedded call option in an equity-linked life insurance contract.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 51 (2012)
    Issue (Month): 1 ()
    Pages: 182-190

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    Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:182-190

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: IB10; IM01; IM10; IM53; Conditional value-at-risk; Dynamic hedging; Stochastic modeling; Quantile hedging; Unit-linked contracts;

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    1. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    2. Laeven, Roger J. A. & Goovaerts, Marc J., 2004. "An optimization approach to the dynamic allocation of economic capital," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 299-319, October.
    3. McGill, Dan M. & Brown, Kyle N. & Haley, John J. & Schieber, Sylvester J., 2004. "Fundamentals of Private Pensions," OUP Catalogue, Oxford University Press, Oxford University Press, edition 8, number 9780199269501, October.
    4. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
    5. Melnikov Alexander & Skornyakova Victoria, 2005. "Quantile hedging and its application to life insurance," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 23(4/2005), pages 301-316, April.
    6. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1505-1518, July.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1443-1471, July.
    10. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(3), pages 195-213, June.
    11. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
    12. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
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