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Optimal investment decisions when time-horizon is uncertain

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  • Blanchet-Scalliet, Christophette
  • El Karoui, Nicole
  • Jeanblanc, Monique
  • Martellini, Lionel

Abstract

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton, R.C., 1971. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373-413], where we allow the conditional distribution function of an agent's time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is affected.

Suggested Citation

  • Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1100-1113
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    References listed on IDEAS

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    1. Merton, Robert C., 1975. "Theory of Finance from the Perspective of Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(4), pages 659-674, November.
    2. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    3. 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.
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    6. Nils H. Hakansson, 1971. "Optimal Entrepreneurial Decisions in a Completely Stochastic Environment," Management Science, INFORMS, vol. 17(7), pages 427-449, March.
    7. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
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