Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities
AbstractWe develop a theory for valuing non-diversifiable mortality risk in an incomplete market by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saá-Requejo [2000. Beyond arbitrage: good deal asset price bounds in incomplete markets. Journal of Political Economy 108, 79-119] and of Björk and Slinko [2006. Towards a general theory of good deal bounds. Review of Finance 10, 221-260] applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 33 (2009)
Issue (Month): 3 (March)
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Web page: http://www.elsevier.com/locate/jedc
Stochastic mortality Pricing Annuities Sharpe ratio Non-linear partial differential equations Market price of risk Equivalent martingale measures;
Other versions of this item:
- 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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
- Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
- Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
- Virginia R. Young, 2007. "Pricing Life Insurance under Stochastic Mortality via the Instantaneous Sharpe Ratio: Theorems and Proofs," Papers 0705.1297, arXiv.org.
- Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736.
- Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
- Schweizer, Martin, 2001. "From actuarial to financial valuation principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 31-47, February.
- Horneff, Wolfram J. & Maurer, Raimond H. & Stamos, Michael Z., 2008. "Life-cycle asset allocation with annuity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3590-3612, November.
- Milevsky, Moshe A. & David Promislow, S., 2001. "Mortality derivatives and the option to annuitise," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 299-318, December.
- M. A. Milevsky & S. D. Promislow & V. R. Young, 2006. "Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 673-686.
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
- Erhan Bayraktar & Virginia Young, 2008.
"Pricing options in incomplete equity markets via the instantaneous Sharpe ratio,"
Annals of Finance,
Springer, vol. 4(4), pages 399-429, October.
- Erhan Bayraktar & Virginia R. Young, 2007. "Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio," Papers math/0701650, arXiv.org, revised Jul 2007.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Ludkovski, Michael & Young, Virginia R., 2008. "Indifference pricing of pure endowments and life annuities under stochastic hazard and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 14-30, February.
- Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
- 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.
- Emilio Bisetti & Carlo A. Favero & Giacomo Nocera & Claudio Tebaldi, 2013. "A Multivariate Model of Strategic Asset Allocation with Longevity Risk," Working Papers 503, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Huang, Yu-Lieh & Tsai, Jeffrey Tzuhao & Yang, Sharon S. & Cheng, Hung-Wen, 2014. "Price bounds of mortality-linked security in incomplete insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 30-39.
- Hua Chen & Michael Sherris & Tao Sun & Wenge Zhu, 2013. "Living With Ambiguity: Pricing Mortality-Linked Securities With Smooth Ambiguity Preferences," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 705-732, 09.
- 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, vol. 51(2), pages 442-448.
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