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Weak Second-Order Conditions of Runge–Kutta Method for Stochastic Optimal Control Problems

Author

Listed:
  • Fikriye Yılmaz

    (Gazi University)

  • Hacer Öz Bakan
  • Gerhard-Wilhelm Weber

    (Poznan University of Technology
    IAM, METU)

Abstract

In this work, we obtain weak order-2 conditions of Runge–Kutta method for the optimal control of stochastic differential equations which occurs in many areas of economics and finance and recently in cognitive sciences and neuroscience. We get the order conditions that a stochastic Runge–Kutta technique must meet to have weak order two by comparing the stochastic expansion of the approximation with the associated Taylor scheme. Moreover, we present numerical examples which verify the theoretical results. We conclude our paper by a summary and an outlook to future research and application.

Suggested Citation

  • Fikriye Yılmaz & Hacer Öz Bakan & Gerhard-Wilhelm Weber, 2024. "Weak Second-Order Conditions of Runge–Kutta Method for Stochastic Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 497-517, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-023-02324-y
    DOI: 10.1007/s10957-023-02324-y
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    References listed on IDEAS

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