Robust Time-Inconsistent Stochastic Linear-Quadratic Control

41 Pages Posted: 8 May 2018 Last revised: 29 Jul 2019

See all articles by Bingyan Han

Bingyan Han

Department of Statistics, The Chinese University of Hong Kong

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: February 1, 2019

Abstract

This paper studies stochastic linear-quadratic control problems for an ambiguity-adverse agent with a time-inconsistent objective. We allow the agent to incorporate disturbances into the state's drift or choose an alternative model among a set of models equivalent to the reference model, to reflect her ambiguity aversion on the drift coefficient of the state process. We adopt an innovative two-step equilibrium control approach to characterize the robust time-consistent controls and simultaneously preserve the preference order. 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 the portfolio's performance in terms of Sharpe ratio by incorporating robustness.

Keywords: Stochastic Linear-Quadratic Control, Robustness, Model Uncertainty, Time-Inconsistent Cost Function, Forward-Backward Stochastic Differential Equation

Suggested Citation

Han, Bingyan and Pun, Chi Seng and Wong, Hoi Ying, Robust Time-Inconsistent Stochastic Linear-Quadratic Control (February 1, 2019). Available at SSRN: https://ssrn.com/abstract=3167662 or http://dx.doi.org/10.2139/ssrn.3167662

Bingyan Han

Department of Statistics, The Chinese University of Hong Kong ( email )

Shatin, N.T.
Hong Kong

HOME PAGE: http://www.sta.cuhk.edu.hk/People/PhDMPhilStudents.aspx?udt_535_param_detail=396

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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