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On the Gradient Method in One Portfolio Management Problem

Author

Listed:
  • Suriya Kumacheva

    (Department of Economics, St. Petersburg State University, 199034 Saint-Petersburg, Russia)

  • Vitalii Novgorodtcev

    (Department of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 Saint-Petersburg, Russia)

Abstract

This study refines the methodology for solving stochastic optimal control problems with quality criteria that include the sum of the quality functional of the classical formulation and an extremal measure. A two-level optimization solution of these kinds of problems is presented already for the case where the quality functional consists only of the extremal measure. Our study shows the possibility of solving the original time inconsistency problem through solving a two-level optimization problem, where the outer problem is solved by gradient methods since the value function is convex and the inner problem is solved by classical methods. Some experiments were carried out and confirmed the validity of the theory. The results of the study can be applied to the case of portfolio management with quality criteria containing the Conditional Value-at-Risk (CVaR) metric.

Suggested Citation

  • Suriya Kumacheva & Vitalii Novgorodtcev, 2024. "On the Gradient Method in One Portfolio Management Problem," Mathematics, MDPI, vol. 12(19), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3086-:d:1491000
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    References listed on IDEAS

    as
    1. Pieter M. van Staden & Peter A. Forsyth & Yuying Li, 2023. "A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming," Papers 2303.08968, arXiv.org.
    2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    Full references (including those not matched with items on IDEAS)

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