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

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