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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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    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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