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Efficient Hedging For Defaultable Securities And Its Application To Equity-Linked Life Insurance Contracts

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  • ALEXANDER MELNIKOV

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada)

  • AMIR NOSRATI

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada)

Abstract

The paper deals with efficient hedging problem for defaultable securities with multiple default times and nonzero recovery rates. First, we convert the efficient hedging problem into a Neyman–Pearson problem with composite hypothesis against a simple alternative. Then we apply nonsmooth convex duality to provide a solution in the framework of a “defaultable” Black–Scholes model. Moreover, in the case of zero recovery rates, we find a closed form solution for the problem. As an application, it is shown how to use such type of results in pricing equity-linked life insurance contracts. The results are also demonstrated by some numerical examples.

Suggested Citation

  • Alexander Melnikov & Amir Nosrati, 2015. "Efficient Hedging For Defaultable Securities And Its Application To Equity-Linked Life Insurance Contracts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-28, November.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:07:n:s0219024915500478
    DOI: 10.1142/S0219024915500478
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    References listed on IDEAS

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    1. 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.
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    3. Alexander Melnikov & Yuliya Romanyuk, 2008. "Efficient Hedging And Pricing Of Equity-Linked Life Insurance Contracts On Several Risky Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 295-323.
    4. 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.
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    Full references (including those not matched with items on IDEAS)

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