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

Fikriye Yılmaz (), Hacer Öz Bakan () and Gerhard-Wilhelm Weber ()
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Fikriye Yılmaz: Gazi University
Gerhard-Wilhelm Weber: Poznan University of Technology

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 22, 497-517

Abstract: 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.

Keywords: Optimal control; Stochastic differential equations; Weak order Taylor expansion; Runge–Kutta method; 49J53; 49K99; 62P05; 37A50 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02324-y

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