Impulse control of conditional McKean-Vlasov jump diffusions
Abstract
This paper establishes a verification theorem for impulse control problems involving conditional McKean-Vlasov jump diffusions. We obtain a Markovian system by combining the state equation of the problem with the stochastic Fokker-Planck equation for the conditional probability law of the state. We derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control which satisfy the verification theorem.
Cite
@article{arxiv.2301.01506,
title = {Impulse control of conditional McKean-Vlasov jump diffusions},
author = {Nacira Agram and Giulia Pucci and Bernt Oksendal},
journal= {arXiv preprint arXiv:2301.01506},
year = {2023}
}
Comments
19 pages. arXiv admin note: text overlap with arXiv:2207.13994