Equilibria for Time-inconsistent Singular Control Problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866911828240498688 |
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| author | Liang, Zongxia Luo, Xiaodong Yuan, Fengyi |
| author_facet | Liang, Zongxia Luo, Xiaodong Yuan, Fengyi |
| contents | We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For the problem with non-exponential discount, both sufficient and necessary conditions are derived, providing a thorough mathematical characterization of the equilibrium. Specifically, the equilibrium can be characterized by an extended HJB system, which is a coupled system of non-local parabolic equations with free boundaries. Finally, by showing the existence of classical solutions to the extended HJB system, the existence of equilibria is established under some additional assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09198 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equilibria for Time-inconsistent Singular Control Problems Liang, Zongxia Luo, Xiaodong Yuan, Fengyi Optimization and Control We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For the problem with non-exponential discount, both sufficient and necessary conditions are derived, providing a thorough mathematical characterization of the equilibrium. Specifically, the equilibrium can be characterized by an extended HJB system, which is a coupled system of non-local parabolic equations with free boundaries. Finally, by showing the existence of classical solutions to the extended HJB system, the existence of equilibria is established under some additional assumptions. |
| title | Equilibria for Time-inconsistent Singular Control Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2310.09198 |