Optimal Two-Mode Switching with Setup Costs for a Controlled Ornstein--Uhlenbeck Process

Hongkun Xia, Dacheng Yao · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27552 · open-access PDF

Abstract

We study an infinite-horizon discounted optimal switching problem for an Ornstein--Uhlenbeck process whose mean-reversion level can be switched between two values. Switching incurs positive, potentially asymmetric fixed costs, and the mode with the higher mean-reversion level entails an additional running cost. The revenue rate is proportional to the positive part of the state. We characterize the value function and identify parameter conditions under which an optimal policy either remains permanently in one mode after a possible costly initial switch or follows a threshold rule. The threshold

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