Dufour, Francois, Piunovskiy, Alexey 
ORCID: 0000-0002-9683-4856 and Plakhov, Alexander
(2022)
On the equivalence of the integral and differential Bellman equations in impulse control problems.
International Journal of Control, 95 (1).
pp. 173-186.
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Abstract
When solving optimal impulse control problems, one can use the dynamic programming approach in two different ways: at each time moment, one can make the decision whether to apply a particular type of impulse, leading to the instantaneous change of the state, or apply no impulses at all; or, otherwise, one can plan an impulse after a certain interval, so that the length of that interval is to be optimised along with the type of that impulse. The first method leads to the differential Bellman equation, while the second method leads to the integral Bellman equation. The target of the current article is to prove the equivalence of those Bellman equations in many specific models. Those include abstract dynamical systems, controlled ordinary differential equations, piece-wise deterministic Markov processes and continuous-time Markov decision processes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Dynamical system, Optimal stopping, Impulse control, Dynamic programming, Total cost |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 20 Jul 2020 08:04 |
| Last Modified: | 16 Nov 2023 22:16 |
| DOI: | 10.1080/00207179.2020.1786766 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3094361 |
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