2017/02/18 by Salvatore Federico, Federico, Salvatore, Fausto Gozzi +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #49L20 #49N35 #65H15 #70H20 #93E20 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #msc:49L20 #msc:49N35 #msc:65H15 #msc:70H20 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1702.05642
openalex publication_date 2017/02/18 · arxiv created 2018/04/30 · arxiv updated 2018/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.