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Optimal investments for the standard maximization problem with non-concave utility function in complete market model

Author

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  • Olena Bahchedjioglou

    (Taras Shevchenko National University of Kyiv)

  • Georgiy Shevchenko

    (Kyiv School of Economics)

Abstract

We study the standard utility maximization problem for a non-decreasing upper-semicontinuous utility function satisfying mild growth assumption. In contrast to the classical setting, we do not impose the assumption that the utility function is concave. By considering the concave envelope, or concavification, of the utility function, we identify the optimal solution for the optimization problem. We also construct the optimal solution for the constrained optimization problem, where the final endowment is bounded from above by a discrete random variable. We present several examples illustrating that our assumptions cannot be totally avoided.

Suggested Citation

  • Olena Bahchedjioglou & Georgiy Shevchenko, 2022. "Optimal investments for the standard maximization problem with non-concave utility function in complete market model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 163-181, February.
    • Handle: RePEc:spr:mathme:v:95:y:2022:i:1:d:10.1007_s00186-022-00774-0
    DOI: 10.1007/s00186-022-00774-0
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    References listed on IDEAS

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    1. 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.
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    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Alexander Schied, 2005. "Optimal Investments for Robust Utility Functionals in Complete Market Models," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 750-764, August.
    5. Jennifer N. Carpenter, 2000. "Does Option Compensation Increase Managerial Risk Appetite?," Journal of Finance, American Finance Association, vol. 55(5), pages 2311-2331, October.
    6. Schied, Alexander & Wu, Ching-Tang, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers 2005-025, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. 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 247-257, August.
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    Cited by:

    1. Ariel Neufeld & Julian Sester, 2024. "Non-concave distributionally robust stochastic control in a discrete time finite horizon setting," Papers 2404.05230, arXiv.org.

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