ﻻ يوجد ملخص باللغة العربية
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.
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, wit
We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 ($mu$ $otimes$ $mu$) for certain signed matrix measures $mu$ which are not necessarily finite. Such equations can be seen as the in
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and state process
We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision maker is risk aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward
We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly controlled in b