Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries

We establish a generalization of the Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton–Jacobi–Bellman equation associated with an optimal control problem it is possible to build...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 9; p. 953
Main Authors De Vecchi, Francesco C., Mastrogiacomo, Elisa, Turra, Mattia, Ugolini, Stefania
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.05.2021
Subjects
contact symmetries
Control theory
Food science
Martingales
Mechanics
Merton’s optimal portfolio problem
Noether theorem
Optimal control
Partial differential equations
stochastic optimal control
Symmetry
Theorems
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Summary:We establish a generalization of the Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton–Jacobi–Bellman equation associated with an optimal control problem it is possible to build a related local martingale. Moreover, we provide an application of the theoretical results to Merton’s optimal portfolio problem, showing that this model admits infinitely many conserved quantities in the form of local martingales.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9090953