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Dynamic hedging of conditional value-at-risk


  • Melnikov, Alexander
  • Smirnov, Ivan


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.

Suggested Citation

  • Melnikov, Alexander & Smirnov, Ivan, 2012. "Dynamic hedging of conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 182-190.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:1:p:182-190
    DOI: 10.1016/j.insmatheco.2012.03.011

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    References listed on IDEAS

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    Cited by:

    1. Compare, M. & Martini, F. & Zio, E., 2015. "Genetic algorithms for condition-based maintenance optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 244(2), pages 611-623.
    2. Feng, Runhuan & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    3. Barski Michał, 2016. "On the shortfall risk control: A refinement of the quantile hedging method," Statistics & Risk Modeling, De Gruyter, vol. 32(2), pages 125-141, March.
    4. Capiński, Maciej J., 2015. "Hedging Conditional Value at Risk with options," European Journal of Operational Research, Elsevier, vol. 242(2), pages 688-691.

    More about this item


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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


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