scholarly journals On the Noether Theorem for Optimal Control

2002 ◽  
Vol 8 (1) ◽  
pp. 56-63 ◽  
Author(s):  
D.F.M. Torres
Keyword(s):  
Optimal Control ◽  
Noether Theorem

scholarly journals Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 953
Author(s):  
Francesco C. De Vecchi ◽  
Elisa Mastrogiacomo ◽  
Mattia Turra ◽  
Stefania Ugolini
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Local Martingale ◽  
Control Problems ◽  
Noether Theorem ◽  
Jet Bundles ◽  
Portfolio Problem ◽  
Contact Symmetry ◽  
Hamilton Jacobi Bellman

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.

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