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

Yılmaz, Fikriye; Öz Bakan, Hacer; Weber, Gerhard-Wilhelm

doi:10.1007/s10957-023-02324-y

J Optim Theory Appl

2023

DOI: 10.1007/s10957-023-02324-y

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

Fikriye Yılmaz,

Hacer Öz Bakan,

Gerhard-Wilhelm Weber

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Cited by 3 publications

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Pathwise Stochastic Control and a Class of Stochastic Partial Differential Equations

Bhauryal,

Cruzeiro,

Oliveira

2024

J Optim Theory Appl

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In this article, we study a stochastic optimal control problem in the pathwise sense, as initially proposed by Lions and Souganidis in [C. R. Acad. Sci. Paris Ser. I Math., 327 (1998), pp. 735-741]. The corresponding Hamilton-Jacobi-Bellman (HJB) equation, which turns out to be a non-adapted stochastic partial differential equation, is analyzed. Making use of the viscosity solution framework, we show that the value function of the optimal control problem is the unique solution of the HJB equation. When the optimal drift is defined, we provide its characterization. Finally, we describe the associated conserved quantities, namely the space-time transformations leaving our pathwise action invariant.

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Pathwise Stochastic Control and a Class of Stochastic Partial Differential Equations

Bhauryal,

Cruzeiro,

Oliveira

2024

J Optim Theory Appl

View full text Add to dashboard Cite

show abstract

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

Cited by 3 publications

References 30 publications

Pathwise Stochastic Control and a Class of Stochastic Partial Differential Equations

Pathwise Stochastic Control and a Class of Stochastic Partial Differential Equations

Assessing the industry 4.0 strategies for a steel supply chain: SWOT, game theory, and gap analysis

Optimizing energy consumption for blockchain adoption through renewable energy sources

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