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Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

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  • M. A. Milevsky
  • S. D. Promislow
  • V. R. Young
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    Abstract

    We provide an overview of how the law of large numbers breaks down when pricing life-contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per-policy risk and show that it goes to a non-zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non-systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk. Copyright The Journal of Risk and Insurance, 2006.

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    Bibliographic Info

    Article provided by The American Risk and Insurance Association in its journal Journal of Risk & Insurance.

    Volume (Year): 73 (2006)
    Issue (Month): 4 ()
    Pages: 673-686

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    Handle: RePEc:bla:jrinsu:v:73:y:2006:i:4:p:673-686

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    Cited by:
    1. De Waegenaere, A.M.B. & Melenberg, B. & Stevens, R., 2010. "Longevity risk," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4578387, Tilburg University.
      • Anja De Waegenaere & Bertrand Melenberg & Ralph Stevens, 2010. "Longevity Risk," De Economist, Springer, vol. 158(2), pages 151-192, June.
    2. Erhan Bayraktar & Moshe Milevsky & David Promislow & Virginia Young, 2008. "Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities," Papers 0802.3250, arXiv.org.
    3. Tsai, Jeffrey T. & Wang, Jennifer L. & Tzeng, Larry Y., 2010. "On the optimal product mix in life insurance companies using conditional value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 235-241, February.
    4. Huang, Rachel J. & Tsai, Jeffrey T. & Tzeng, Larry Y., 2008. "Government-provided annuities under insolvency risk," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 377-385, December.
    5. Matheus R Grasselli & Sebastiano Silla, 2009. "A policyholder's utility indifference valuation model for the guaranteed annuity option," Papers 0908.3196, arXiv.org.
    6. Helena Aro, 2013. "Systematic and non-systematic mortality risk in pension portfolios," Papers 1307.8020, arXiv.org, revised Jul 2013.
    7. Bauer, Daniel & Börger, Matthias & Ruß, Jochen, 2010. "On the pricing of longevity-linked securities," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 139-149, February.

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