On pricing barrier control in a regime-switching regulated market

Abstract

We study a pricing barrier control problem in a regime-switching regulated market. In doing so, we analyze a class of one-dimensional reflected regime-switching diffusion processes. Such diffusion models arise as the key approximating processes in a regulated financial market system with the presence of regime changes. Our main goal is to determine optimal pricing barriers as solutions of long-run average mean–variance optimization problems. More precisely, the optimal barrier, if exists, will be to maximize the long-run average expected return (i.e. steady-state mean) subject to a selected level of long-run average risk (i.e. steady-state variance).

Keywords:

• Reflected diffusions
• Optimal barriers
• Regulated market
• Regime-switching
• Ergodic control
• Mean–variance optimization

Acknowledgements

We would like to thank the two anonymous reviewers for their valuable suggestions and comments that have much enhanced the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Army Research Office [grant number W911NF1410216] and an NSERC Discovery Grant.