Abstract
We consider the problem of tracking a target whose dynamics is modeled by a continuous Itô semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. A comprehensive list of examples with explicit expressions for the lower bounds is provided.
| Original language | English |
|---|---|
| Pages (from-to) | 2455-2514 |
| Number of pages | 60 |
| Journal | Annals of Applied Probability |
| Volume | 27 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Aug 2017 |
| Externally published | Yes |
Keywords
- Asymptotic lower bound
- Impulse control
- Linear programming
- Occupation measure
- Optimal tracking
- Regular control
- Singular control