Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 86, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s00245-022-09881-0
Keywords
Ergodic singular control; Vanishing discount; Abelian limit; Cesaro limit
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Funding
- National Natural Science Foundation of China [12071031]
- National Science Foundation [DMS-2204240]
- Simons Foundation [523736]
- University of Wisconsin-Milwaukee
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Motivated by applications in natural resource management, risk management, and finance, this paper focuses on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The optimal reward value and control policy are derived using the vanishing discount method under mild conditions. Additionally, the Abelian and Cesaro limits are established, and a direct solution approach is provided.
Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a bounded variation process. Under some mild conditions, the optimal reward value as well as an optimal control policy are derived by the vanishing discount method. Moreover, the Abelian and Cesaro limits are established. Then a direct solution approach is provided at the end of the paper.
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