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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 11 (December)
Pages: 1100-1113

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Handle: RePEc:eee:mateco:v:44:y:2008:i:11:p:1100-1113

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Uncertain time-horizon Dynamic portfolio selection;

References

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  1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  2. Huang, Ming, 2003. "Liquidity shocks and equilibrium liquidity premia," Journal of Economic Theory, Elsevier, vol. 109(1), pages 104-129, March.
  3. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
  4. Hakansson, Nils H, 1969. "Optimal Investment and Consumption Strategies under Risk, an Uncertain Lifetime, and Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 443-66, October.
  5. 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.
  6. Merton, Robert C., 1975. "Theory of Finance from the Perspective of Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(04), pages 659-674, November.
  7. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  8. 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.
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Citations

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Cited by:
  1. I. Duarte & D. Pinheiro & A. A. Pinto & S. R. Pliska, 2011. "Optimal Life Insurance Purchase, Consumption and Investment on a financial market with multi-dimensional diffusive terms," Papers 1102.2263, arXiv.org.
  2. Wu, Huiling & Zeng, Yan & Yao, Haixiang, 2014. "Multi-period Markowitz's mean–variance portfolio selection with state-dependent exit probability," Economic Modelling, Elsevier, vol. 36(C), pages 69-78.
  3. Giulia Di Nunno & Steffen Sjursen, 2013. "Information and optimal investment in defaultable assets," Papers 1312.6032, arXiv.org.
  4. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
  5. Constantinos Kardaras, 2009. "Num\'{e}raire-invariant preferences in financial modeling," Papers 0903.3736, arXiv.org, revised Nov 2010.
  6. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Center of Excellence SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
  7. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
  8. Constantinos Kardaras, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.

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