Robust classical-impulse stochastic control problems in an infinite horizon
This paper establishes a general analytical framework for classical and impulse stochastic control problems in the presence of model uncertainty. We consider a set of dominated models, which are induced by the measures equivalent to that of a reference model. The state process under the reference mo...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/163253 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | This paper establishes a general analytical framework for classical and impulse stochastic control problems in the presence of model uncertainty. We consider a set of dominated models, which are induced by the measures equivalent to that of a reference model. The state process under the reference model is a multidimensional Markov process with multidimensional Brownian motion, controlled by continuous and impulse control variates. We propose quasi-variational inequalities (QVI) associated with the value function of the control problem and prove a verification theorem for the solution to the QVI. With the relative entropy constraints and piecewise linear intervention penalty, we show that the QVI can be degenerated to the non-robust case and it can be solved via the solution to a free boundary problem. To illustrate the tractability of the proposed framework, we apply it to a linear-quadratic setting, which covers a broad class of problems including robust mean-reverting inventory controls. |
|---|