Robust time-inconsistent stochastic linear-quadratic control with drift disturbance
This paper studies stochastic linear-quadratic control with a time-inconsistent objective and worst-case drift disturbance. We allow the agent to introduce disturbances to reflect her uncertainty about the drift coefficient of the controlled state process. We adopt a two-step equilibrium control app...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/163191 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | This paper studies stochastic linear-quadratic control with a time-inconsistent objective and worst-case drift disturbance. We allow the agent to introduce disturbances to reflect her uncertainty about the drift coefficient of the controlled state process. We adopt a two-step equilibrium control approach to characterize the robust time-consistent controls, which can preserve the order of preference. Under a general framework allowing random parameters, we derive a sufficient condition for equilibrium controls using the forward-backward stochastic differential equation approach. We also provide analytical solutions to mean-variance portfolio problems for various settings. Our empirical studies confirm the improvement in portfolio’s performance in terms of out-of-sample Sharpe ratio by incorporating with robustness. |
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