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Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems

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  • Esben Kryger
  • Maj-Britt Nordfang
  • Mogens Steffensen

Abstract

We present a modified verification theorem for the equilibrium control of a general class of portfolio problems. The general class of portfolio problems studied in this paper, is characterized by an objective where the investor seeks to maximize a functional of two conditional expectations of terminal wealth. The objective functional is allowed to be non-linear in the conditional expectations, and thus the problem class is in general terms time-inconsistent. In addition, we provide a corrected proof of the verification theorem and apply the theorem to a number of quadratic, time-inconsistent portfolio problems and determine their solutions. Some of the quadratic portfolio problems have not previously been solved analytically.

Suggested Citation

  • Esben Kryger & Maj-Britt Nordfang & Mogens Steffensen, 2020. "Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 405-438, June.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:3:d:10.1007_s00186-019-00687-5
    DOI: 10.1007/s00186-019-00687-5
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    References listed on IDEAS

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    Cited by:

    1. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    2. Fahrenwaldt, Matthias Albrecht & Jensen, Ninna Reitzel & Steffensen, Mogens, 2020. "Nonrecursive separation of risk and time preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 95-108.
    3. Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    4. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    5. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.

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