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.

Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries / F.C. De Vecchi, E. Mastrogiacomo, M. Turra, S. Ugolini. - In: MATHEMATICS. - ISSN 2227-7390. - 9:9(2021 Apr 24), pp. 953.1-953.34. [10.3390/math9090953]

Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries

S. Ugolini
Ultimo
2021-04-24

Abstract

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.
Noether theorem; stochastic optimal control; contact symmetries; Merton's optimal portfolio problem
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/842356
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