{"ID":2856207,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11158","arxiv_id":"2510.11158","title":"Optimal Policy Characterization for a Class of Multi-Dimensional Ergodic Singular Stochastic Control Problems","abstract":"In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost of control is proportional to the magnitude of adjustments. This paper characterizes the optimal policy and the value in a class of multi-dimensional ergodic singular stochastic control problems. These problems involve a linearly controlled one-dimensional stochastic differential equation, whose coefficients, along with the cost functional to be optimized, depend on a multi-dimensional uncontrolled process Y. We first provide general verification theorems providing an optimal control in terms of a Skorokhod reflection at Y-dependent free boundaries, which emerge from the analysis of an auxiliary Dynkin game. We then fully solve two two-dimensional optimal inventory management problems. To the best of our knowledge, this is the first paper to establish a connection between multi-dimensional ergodic singular stochastic control and optimal stopping, and to exploit this connection to achieve a complete solution in a genuinely two-dimensional setting.","short_abstract":"In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost of control is proportional to the magnitude of adjustments. This paper characteri...","url_abs":"https://arxiv.org/abs/2510.11158","url_pdf":"https://arxiv.org/pdf/2510.11158v1","authors":"[\"Alessandro Calvia\",\"Federico Cannerozzi\",\"Giorgio Ferrari\"]","published":"2025-10-13T08:50:50Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}