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Consumption, investment and life insurance strategies with heterogeneous discounting

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Author Info

  • Albert de-Paz
  • Jesus Marin-Solano
  • Jorge Navas
  • Oriol Roch

    (Universitat de Barcelona)

Abstract

In this paper we analyze how the optimal consumption, investment and life insur- ance rules are modified by the introduction of a class of time-inconsistent preferences. In particular, we account for the fact that an agents preferences evolve along the planning horizon according to her increasing concern about the bequest left to her descendants and about her welfare at retirement. To this end, we consider a stochas- tic continuous time model with random terminal time for an agent with a known distribution of lifetime under heterogeneous discounting. In order to obtain the time- consistent solution, we solve a non-standard dynamic programming equation. For the case of CRRA and CARA utility functions we compare the explicit solutions for the time-inconsistent and the time-consistent agent. The results are illustrated numeri- cally.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 277.

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Length: 0 pages
Date of creation: 2012
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Handle: RePEc:bar:bedcje:2012277

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es
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  1. 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.
  2. Karp, Larry, 2004. "Non-constant discounting in continuous time," CUDARE Working Paper Series 0969, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  3. Leung, S.F., 1992. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," RCER Working Papers 323, University of Rochester - Center for Economic Research (RCER).
  4. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
  5. Holger Kraft, 2003. "Elasticity approach to portfolio optimization," Computational Statistics, Springer, vol. 58(1), pages 159-182, 09.
  6. 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.
  7. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
  8. Ekeland, Ivar & Mbodji, Oumar & Pirvu, Traian A., 2012. "Time-Consistent Portfolio Management," Economics Papers from University Paris Dauphine 123456789/11473, Paris Dauphine University.
  9. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
  10. de-Paz, Albert & Marín-Solano, Jesús & Navas, Jorge, 2013. "A consumption–investment problem with heterogeneous discounting," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 221-232.
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