Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper, we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal control problems. The method applies in the case of additively controlled Ornstein-Uhlenbeck processes, when the associated Hamilton-Jacobi-Bellman (HJB) equation admits a mild solution (in the sense of [J. Differential Equations 262 (2017) 3343-3389]). The main methodological novelty of our result relies on the fact that it is not needed to prove, as in previous literature (see, e.g., [Comm. Partial Differential Equations 20 (1995) 775-826]), that the mild solution is a strong solution, that is, a suitable limit of classical solutions of approximating HJB equations. To achieve the goal, we prove a new type of Dynkin formula, which is the key tool for the proof of our main result.
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|Titolo:||Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula|
FEDERICO, SALVATORE (Corresponding)
|Citazione:||Federico, S., & Gozzi, F. (2018). Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula. THE ANNALS OF APPLIED PROBABILITY, 28(6), 3558-3599.|
|Appare nelle tipologie:||1.1 Articolo in rivista|