Robust time-inconsistent stochastic linear-quadratic control with drift disturbance

• Main Authors: Han, Bingyan, Pun, Chi Seng, Wong, Hoi Ying
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Robust Control; Stochastic Linear-Quadratic Control
• Online Access: https://hdl.handle.net/10356/163191
• Institution: Nanyang Technological University

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.