Noether theorem in stochastic optimal control problems via contact symmetries

Francesco C. De Vecchi, Elisa Mastrogiacomo, Mattia Turra and Stefania Ugolini

Papers from arXiv.org

Abstract: 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 Hamilton-Jacobi-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 form of local martingales.

Date: 2021-02
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Mathematics (MDPI) 9, no. 9 (2021)

Downloads: (external link)
http://arxiv.org/pdf/2102.03172 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2102.03172

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().