Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula

Salvatore Federico; Fausto Gozzi

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arXiv · 1702.05642

Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula

Salvatore Federico·Fausto Gozzi

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Abstract

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. The main methodological novelty of our result relies on the fact that it is not needed to prove, as in previous literature, that the mild solution is a strong solution, i.e. a suitable limit of classical solutions of the HJB equation. To achieve our 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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Salvatore Federico, Fausto Gozzi. 2017-02-18. Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula. https://arxiv.org/abs/1702.05642

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