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Quantile hedging for equity-linked contracts

Author

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  • Klusik, Przemyslaw
  • Palmowski, Zbigniew

Abstract

We consider an equity-linked contract whose payoff depends on the lifetime of the policy holder and the stock price. We provide the best strategy for an insurance company assuming limited capital for the hedging. The main idea of the proof consists in reducing the construction of such strategies for a given claim to a problem of superhedging for a modified claim, which is the solution to a static optimization problem of the Neyman-Pearson type. This modified claim is given via some sets constructed in an iterative way. Some numerical examples are also given.

Suggested Citation

  • Klusik, Przemyslaw & Palmowski, Zbigniew, 2011. "Quantile hedging for equity-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 280-286, March.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:280-286
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    References listed on IDEAS

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    1. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
    2. 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, vol. 3(3), pages 195-213, June.
    3. Melnikov Alexander & Skornyakova Victoria, 2005. "Quantile hedging and its application to life insurance," Statistics & Risk Modeling, De Gruyter, vol. 23(4/2005), pages 301-316, April.
    4. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 21(1), pages 35-63, June.
    5. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
    6. Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(02), pages 275-297, November.
    7. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
    8. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
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    Cited by:

    1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
    2. Klusik Przemyslaw, 2014. "Hedging of equity-linked with maximal success factor," Papers 1405.0732, arXiv.org.
    3. Przemys{l}aw Klusik, 2014. "Market risk modelling in Solvency II regime and hedging options not using underlying," Papers 1405.1212, arXiv.org.

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