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Optimal consumption with labor income and borrowing constraints for recursive preferences

Author

Listed:
  • Dirk Becherer

    (Institute of Mathematics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany)

  • Wilfried Kuissi-Kamdem

    (Department of Mathematics, University of Rwanda, Kigali 4285, Rwanda)

  • Olivier Menoukeu-Pamen

    (Institute of Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom)

Abstract

We study the optimal consumption and investment problem for an investor with liquidity constraints who has isoelastic recursive Epstein-Zin utility preferences and receives a stochastic stream of income. We characterize the optimal consumption strategy as well as the terminal wealth for recursive utility under dynamic liquidity constraints, which prevent the investor to borrow against his stochastic future income. Using duality and backward SDE methods in a possibly non-Markovian diffusion model for the financial market, this gives rise to an interplay of singular control and optimal stopping problems. Our analysis extends to more general liquidity constraints.

Suggested Citation

  • Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    • Handle: RePEc:hal:wpaper:hal-04017143
    Note: View the original document on HAL open archive server: https://hal.science/hal-04017143
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    References listed on IDEAS

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    More about this item

    Keywords

    Liquidity constraints; Optimal consumption; Stochastic income; Epstein-Zin recursive utility; Duality; Optimal stopping; Singular control; Reflected BSDE;
    All these keywords.

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