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The role of longevity bonds in optimal portfolios

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Menoncin, Francesco

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Abstract

We study the optimal consumption and portfolio for an agent maximizing the expected utility of his intertemporal consumption in a financial market with: (i) a riskless asset, (ii) a stock, (iii) a bond as a derivative on the stochastic interest rate, and (iv) a longevity bond whose coupons are proportional to the population (stochastic) survival rate. With a force of mortality instantaneously uncorrelated with the interest rate (but not necessarily independent), we demonstrate that the wealth invested in the longevity bond must be taken from the ordinary bond and the riskless asset proportionally to the duration of the two bonds. This result is valid for both a complete and an incomplete financial market.

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

Volume (Year): 42 (2008)
Issue (Month): 1 (February)
Pages: 343-358
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Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:343-358

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

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  1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  4. Lioui, Abraham & Poncet, Patrice, 2001. "On optimal portfolio choice under stochastic interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1841-1865, November. [Downloadable!] (restricted)
  5. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(01), pages 63-91, March. [Downloadable!]
  6. Menoncin, Francesco, 2002. "Optimal portfolio and background risk: an exact and an approximated solution," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 249-265, October. [Downloadable!] (restricted)
  7. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487. [Downloadable!] (restricted)
  8. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December. [Downloadable!] (restricted)
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  9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August. [Downloadable!] (restricted)
  10. Wachter, Jessica A., 2003. "Risk aversion and allocation to long-term bonds," Journal of Economic Theory, Elsevier, vol. 112(2), pages 325-333, October. [Downloadable!] (restricted)
  11. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 141-61. [Downloadable!] (restricted)
  12. George Chacko & Luis M. Viceira, 1999. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," NBER Working Papers 7377, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Thomas Post, 2009. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality," SFB 649 Discussion Papers SFB649DP2009-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Amedeo Fossati & Rosella Levaggi, 2008. "Delay is not the answer: waiting time in health care & income redistribution," Working Papers 0801, University of Brescia, Department of Economics. [Downloadable!]
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