Robust Mean-Variance Portfolio Selection with State-Dependent Ambiguity Aversion and Risk Aversion: A Closed-loop Approach

27 Pages Posted: 8 Jan 2019 Last revised: 11 Sep 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: December 24, 2018

Abstract

This paper studies a class of robust mean-variance portfolio selection problems with state-dependent risk aversion. Model uncertainty, in the sense of considering alternative dominated models, is introduced to the problem to reflect the investor's ambiguity aversion. To characterize the robust portfolios, we consider closed-loop equilibrium control and spike variation approaches. Moreover, we show that the closed-loop equilibrium strategy exists and is unique under some technical conditions. That partially addresses the open problem left in Björk et al. (2017, Finance Stoch.) and Pun (2018, Automatica). By using the necessary and sufficient condition for the equilibrium, we manage to derive the analytical form of the equilibrium strategy via the unique solution to a nonlinear ordinary differential equation system. To validate the proposed closed-loop framework, we show that when there is no ambiguity, our equilibrium strategy is reduced to the strategy in Björk et al. (2014, Math. Finance), which cannot be deduced under the open-loop control framework.

Keywords: Closed-Loop Control, Robust Mean-Variance Portfolio Selection, State-Dependence, Time-Inconsistency, Model Uncertainty

JEL Classification: C72, C73, D81, G11

Suggested Citation

Han, Bingyan and Pun, Chi Seng and Wong, Hoi Ying, Robust Mean-Variance Portfolio Selection with State-Dependent Ambiguity Aversion and Risk Aversion: A Closed-loop Approach (December 24, 2018). Available at SSRN: https://ssrn.com/abstract=3306305 or http://dx.doi.org/10.2139/ssrn.3306305

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
94
Abstract Views
582
rank
332,387
PlumX Metrics