In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Supported in part by the European Union under Grant Agreement “Multi-ITN STRIKE-Novel Methods in Computational Finance”. Fund Project No. 304617 Marie Curie Research Training Network.