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

Date

2023-01-01

Author

YILMAZ, FİKRİYE NURAY
Öz Bakan, Hacer
Weber, Gerhard Wilhelm

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Optimal control, Runge–Kutta method, Stochastic differential equations, Weak order Taylor expansion

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85177693480&origin=inward
https://hdl.handle.net/11511/106877

Collections

Graduate School of Applied Mathematics, Article