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Optimal Consumption Under Deterministic Income

Author

Listed:
  • Julia Eisenberg

    (Vienna University of Technology)

  • Peter Grandits

    (Vienna University of Technology)

  • Stefan Thonhauser

    (University of Lausanne)

Abstract

We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon. Via the Hamilton–Jacobi–Bellman approach, we prove the existence and the uniqueness of the solution to the considered problem in the viscosity sense. Furthermore, we derive an algorithm for explicit calculation of the value function and optimal strategy. It turns out that the value function is in general not continuous. The method is illustrated by two examples.

Suggested Citation

  • Julia Eisenberg & Peter Grandits & Stefan Thonhauser, 2014. "Optimal Consumption Under Deterministic Income," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 255-279, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0320-x
    DOI: 10.1007/s10957-013-0320-x
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    References listed on IDEAS

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    1. Amman, Hans, 1996. "Numerical methods for linear-quadratic models," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 13, pages 587-618, Elsevier.
    2. Agnès Sulem, 1986. "Explicit Solution of a Two-Dimensional Deterministic Inventory Problem," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 134-146, February.
    3. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    4. Dorfman, Robert, 1969. "An Economic Interpretation of Optimal Control Theory," American Economic Review, American Economic Association, vol. 59(5), pages 817-831, December.
    5. Dixit, Avinash K., 1990. "Optimization in Economic Theory," OUP Catalogue, Oxford University Press, edition 2, number 9780198772101.
    6. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    7. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
    8. 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.
    9. Kendrick, David A., 2005. "Stochastic control for economic models: past, present and the paths ahead," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 3-30, January.
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    Cited by:

    1. Roy Cerqueti & Daniele Marazzina & Marco Ventura, 2016. "Optimal Investment in Research and Development Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 296-309, January.
    2. Peter Grandits, 2016. "Optimal Consumption Until Ruin for an Endowment Described by an Autonomous ODE for an Infinite Time Horizon," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 953-968, August.
    3. Julia Eisenberg, 2016. "Deterministic Income with Deterministic and Stochastic Interest Rates," Papers 1603.09519, arXiv.org.
    4. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2022. "Optimal dividends under a drawdown constraint and a curious square-root rule," Papers 2206.12220, arXiv.org.
    5. Hansjörg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividends under a drawdown constraint and a curious square-root rule," Finance and Stochastics, Springer, vol. 27(2), pages 341-400, April.

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