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arXiv · 2411.05488

Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics

Andrea Iannucci·Dan Crisan·Thomas Cass
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Abstract

In this work, we investigate the degeneracy problem in pathwise control, extending the framework developed in \cite{allan2020pathwise} to a more general class of driving signals and a broader set of admissible controls. Our approach consists in choosing admissible controls from a suitable class of H\"older-continuous paths. This leads naturally to the use of fractional derivatives and transforms the original control equation into a fractional dynamics system. Within this setting, we derive sufficient conditions ensuring that the control problem remains non-degenerate. We then build on the analysis developed in \cite{gomoyunov2020dynamic,gomoyunov2020theory,gomoyunov2021viscosity} to study the resulting value function and the associated Hamilton--Jacobi--Bellman equation.

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Andrea Iannucci, Dan Crisan, Thomas Cass. 2024-11-08. Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics. https://arxiv.org/abs/2411.05488

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