  The classical mean-variance portfolio selection problem induces
time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To
overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the
game theoretical approach and look for (sub-game perfect Nash) equilibrium
strategies, which is solved from the corresponding partial differential
equations (PDE) system. In their model, the investor perfectly knows the drift
and volatility of the assets. However, in reality investors only have an
estimate on them, e.g, a 95% confidence interval. In this case, some literature
(e.g., Pham, Wei and Zhou (2022)) derives the optimal precommited strategy
under the worst parameters, which is the robust control. The relation between
the equilibrium strategy and the PDE system has not been justified when
incorporating robust control. In this paper, we consider a general dynamic
mean-variance framework and propose a novel definition of the robust
equilibrium strategy. Under our definition, a classical solution to the
corresponding PDE system implies a robust equilibrium strategy. We then
explicitly solve for some special examples.
