Stochastic optimal control problems with delays in the state and in the control via viscosity solutions and applications to optimal advertising and optimal investment problems

Autor:	de Feo, Filippo
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs Mathematics - Probability 49L25 93E20 60H15 49L20 35R15 49L12 34K50
Druh dokumentu:	Working Paper
Popis:	In this manuscript we consider optimal control problems of stochastic differential equations with delays in the state and in the control. First, we prove an equivalent Markovian reformulation on Hilbert spaces of the state equation. Then, using the dynamic programming approach for infinite-dimensional systems, we prove that the value function is the unique viscosity solution of the infinite-dimensional Hamilton-Jacobi-Bellman equation. We apply these results to problems coming from economics: stochastic optimal advertising problems and stochastic optimal investment problems with time-to-build. Comment: arXiv admin note: substantial text overlap with arXiv:2302.08809
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.14506 Zobrazit plný text záznamu View this record from Arxiv