Abstract
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 Cesàro limits are established. Then a direct solution approach is provided at the end of the paper.
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The authors would like to express their appreciation for the insightful comments by the referee, which improved the paper’s results and exposition.
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F. Xi: The research of this author was supported in part by the National Natural Science Foundation of China under Grant 12071031. G. Yin: The research of this author was supported in part by the National Science Foundation under Grant DMS-2204240. C. Zhu: The research of this author was supported in part by the Simons Foundation under Grant 523736, and in part by a DIG award from the University of Wisconsin-Milwaukee.
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Kunwai, K., Xi, F., Yin, G. et al. On an Ergodic Two-Sided Singular Control Problem. Appl Math Optim 86, 26 (2022). https://doi.org/10.1007/s00245-022-09881-0
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DOI: https://doi.org/10.1007/s00245-022-09881-0