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A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market

Author

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  • Vandaele, Nele
  • Vanmaele, Michèle

Abstract

In [Riesner, M., 2006. Hedging life insurance contracts in a Lévy process financial market. Insurance Math. Econom. 38, 599-608] the (locally) risk-minimizing hedging strategy for unit-linked life insurance contracts is determined in an incomplete financial market driven by a Lévy process. The considered risky asset is not a martingale under the original measure and therefore, a change of measure to the minimal martingale measure is performed. The goal of this paper is to show that the risk-minimizing hedging strategy under the new martingale measure which is found in the paper cited above is not the locally risk-minimizing strategy under the original measure. Finally, the real locally risk-minimizing strategy is derived and a relationship between the number of risky assets held in the proposed portfolio cited in the above-mentioned paper and the one proposed here is given.

Suggested Citation

  • Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1128-1137
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    References listed on IDEAS

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    1. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    2. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
    3. Riesner, Martin, 2007. "Locally Risk-minimizing Hedging of Insurance Payment Streams," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(01), pages 67-91, May.
    4. repec:spr:compst:v:50:y:1999:i:2:p:339-350 is not listed on IDEAS
    5. Riesner, Martin, 2006. "Hedging life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 599-608, June.
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    Citations

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    Cited by:

    1. Delong, Lukasz, 2010. "An optimal investment strategy for a stream of liabilities generated by a step process in a financial market driven by a Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 278-293, December.
    2. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    3. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2015. "Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 47-60.
    4. Pansera, Jérôme, 2012. "Discrete-time local risk minimization of payment processes and applications to equity-linked life-insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 1-11.
    5. repec:bla:jrinsu:v:84:y:2017:i:1:p:209-238 is not listed on IDEAS
    6. Choulli, Tahir & Vandaele, Nele & Vanmaele, Michèle, 2010. "The Föllmer-Schweizer decomposition: Comparison and description," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 853-872, June.
    7. repec:eee:insuma:v:76:y:2017:i:c:p:149-163 is not listed on IDEAS

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