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Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints


  • Claus Munk

    (Odense University, Denmark)


We examine the optimal consumption and portfolio choice of an investor having an initial wealth endowment and an uncertain stream of income from non-traded assets. The income stream is not spanned by traded assets, and the investor is not allowed to borrow against future income, so the financial market is incomplete. We solve the corresponding stochastic control problem numerically with the Markov chain approximation method. In particular, we find that the implicit value, the agent attaches to an uncertain income stream, can be much smaller in this incomplete market than it is in the complete market.

Suggested Citation

  • Claus Munk, 1997. "Optimal Consumption/Investment Policies with Undiversifiable Income Risk and Borrowing Constraints," Finance 9712003, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:9712003
    Note: Type of Document - ; to print on PostScript; pages: 24 ; figures: included

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    References listed on IDEAS

    1. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    2. 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.
    3. Hindy, Ayman & Huang, Chi-fu & Zhu, Steven H., 1997. "Numerical analysis of a free-boundary singular control problem in financial economics," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 297-327.
    4. Darrell Duffie & Thaleia Zariphopoulou, 1993. "Optimal Investment With Undiversifiable Income Risk," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 135-148.
    5. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    6. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
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    Cited by:

    1. Claus Munk, 1997. "No-Arbitrage Bounds on Contingent Claims Prices with Convex Constraints on the Dollar Investments of the Hedge Portfolio," Finance 9712006, EconWPA.

    More about this item


    optimal consumption and portfolio policies; undiversifiable income risk; borrowing constraints; wealth equivalent of income; Markov chain approximation;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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