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Noether theorem in stochastic optimal control problems via contact symmetries

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 نشر من قبل Francesco Carlo De Vecchi
 تاريخ النشر 2021
  مجال البحث
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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 Mertons optimal portfolio problem, showing that this model admits infinitely many conserved quantities in the form of local martingales.



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