Abstract
We study optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in case of partial information control. One important novelty of our problem is represented by the introduction of general mean-field operators, acting on both the controlled state process and the control process. We first formulate a sufficient and a necessary maximum principle for this type of control. We then prove the existence and uniqueness of the solution of such general forward and backward mean-field stochastic partial differential equations. We apply our results to find the explicit optimal control for an optimal harvesting problem.
| Original language | English |
|---|---|
| Pages (from-to) | 549-584 |
| Number of pages | 26 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 176 |
| Issue number | 3 |
| Early online date | 20 Feb 2018 |
| DOIs | |
| Publication status | Published - Mar 2018 |
Keywords
- Mean-field backward stochastic partial differential equation
- Mean-field stochastic partial differential equation
- Optimal control
- Stochastic maximum principles