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Optimization of consumption with labor income


  • Nicole El Karoui

    (Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, place Jussieu, F-75252 Paris Cedex 05, France)

  • Monique Jeanblanc-Picqué

    (Equipe d'Analyse et Probabilités, Université d'Evry, Boulevard des Coquibus, F-91025 Evry Cedex, France Manuscript)


We present the solution of a portfolio optimization problem for an economic agent endowed with a stochastic insurable stream, under a liquidity constraint over the time interval [0,T]. Generally, the existence of labor income complicates the agent's decisions. Moreover, in the real world the economic agents are restricted in their ability to borrow against their future labor income. We deal with this kind of liquidity constraint following the lines of American option valuation which allows us to give a precise characterization of the optimal consumption as well as the terminal wealth. In a Markovian case, with infinite horizon and HARA utility, we obtain a closed form solution.

Suggested Citation

  • Nicole El Karoui & Monique Jeanblanc-Picqué, 1998. "Optimization of consumption with labor income," Finance and Stochastics, Springer, vol. 2(4), pages 409-440.
  • Handle: RePEc:spr:finsto:v:2:y:1998:i:4:p:409-440
    Note: received: December 1996; final version received: August 1997

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