Time-Inconsistent Singular Control Problems with a Running Minimum Process
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914622695538688 |
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| author | Dai, Rui Guan, Guohui Liang, Zongxia Luo, Xiaodong |
| author_facet | Dai, Rui Guan, Guohui Liang, Zongxia Luo, Xiaodong |
| contents | This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions than those imposed in the existing literature, and we obtain a stronger notion of equilibrium by enlarging the class of feasible perturbations. We first establish the mathematical foundations of the framework by proving the existence and uniqueness of strong solutions to a class of Skorokhod reflection problems involving the running minimum and by characterizing admissible singular control laws. We further demonstrate the existence of an equilibrium through a dividend problem, where the running minimum leads to a highly coupled and nonlinear differential-algebraic system. For this problem, we prove the monotonicity and local concavity of the dividend boundary, thereby providing a mathematical explanation for dividend smoothing and scarring effects. Numerical simulations confirm the robustness of the equilibrium across a wide range of parameter values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19914 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time-Inconsistent Singular Control Problems with a Running Minimum Process Dai, Rui Guan, Guohui Liang, Zongxia Luo, Xiaodong Optimization and Control This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions than those imposed in the existing literature, and we obtain a stronger notion of equilibrium by enlarging the class of feasible perturbations. We first establish the mathematical foundations of the framework by proving the existence and uniqueness of strong solutions to a class of Skorokhod reflection problems involving the running minimum and by characterizing admissible singular control laws. We further demonstrate the existence of an equilibrium through a dividend problem, where the running minimum leads to a highly coupled and nonlinear differential-algebraic system. For this problem, we prove the monotonicity and local concavity of the dividend boundary, thereby providing a mathematical explanation for dividend smoothing and scarring effects. Numerical simulations confirm the robustness of the equilibrium across a wide range of parameter values. |
| title | Time-Inconsistent Singular Control Problems with a Running Minimum Process |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.19914 |