Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries

@inproceedings{DeVecchi2021NoetherTI,
  title={Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries},
  author={Francesco C. De Vecchi and Elisa Mastrogiacomo and Mattia Turra and Stefania Ugolini},
  year={2021}
}
We establish a generalization of 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 HamiltonJacobi-Bellman equation associated to 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… 
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