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Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates

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  • Ludkovski, Michael
  • Young, Virginia R.
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    Abstract

    We study indifference pricing of mortality contingent claims in a fully stochastic model. We assume both stochastic interest rates and stochastic hazard rates governing the population mortality. In this setting we compute the indifference price charged by an insurer that uses exponential utility and sells k contingent claims to k independent but homogeneous individuals. Throughout we focus on the examples of pure endowments and temporary life annuities. We begin with a continuous-time model where we derive the linear pdes satisfied by the indifference prices and carry out extensive comparative statics. In particular, we show that the price-per-risk grows as more contracts are sold. We then also provide a more flexible discrete-time analog that permits general hazard rate dynamics. In the latter case we construct a simulation-based algorithm for pricing general mortality-contingent claims and illustrate with a numerical example.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 1 (February)
    Pages: 14-30

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:14-30

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    Web page: http://www.elsevier.com/locate/inca/505554

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    1. Olivieri, Annamaria, 2001. "Uncertainty in mortality projections: an actuarial perspective," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(2), pages 231-245, October.
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    10. Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(3), pages 299-318, December.
    11. Marek Musiela & Thaleia Zariphopoulou, 2004. "A valuation algorithm for indifference prices in incomplete markets," Finance and Stochastics, Springer, Springer, vol. 8(3), pages 399-414, 08.
    12. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, Elsevier, vol. 8(3), pages 393-411, November.
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    14. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 29(10), pages 1737-1764, October.
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    Cited by:
    1. Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(3), pages 676-691, March.
    2. Boualem Djehiche & Bj\"orn L\"ofdahl, 2014. "Risk aggregation and stochastic claims reserving in disability insurance," Papers, arXiv.org 1401.3589, arXiv.org, revised Aug 2014.
    3. Ballestra, Luca Vincenzo & Ottaviani, Massimiliano & Pacelli, Graziella, 2012. "An operator splitting harmonic differential quadrature approach to solve Young’s model for life insurance risk," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(2), pages 442-448.
    4. Ma, Jin & Yun, Youngyun, 2010. "Correlated intensity, counter party risks, and dependent mortalities," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(3), pages 337-351, December.
    5. Biffis, Enrico & Blake, David & Pitotti, Lorenzo & Sun, Ariel, 2011. "The cost of counterparty risk and collateralization in longevity swaps," MPRA Paper 35740, University Library of Munich, Germany.
    6. Thomas Post, 2009. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2009-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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