  In this paper, both dynamic mean-variance portfolio selection problems and
dynamic variance hedging problems are discussed under non-Markovian framework.
Explicit closed-loop equilibrium strategies of these problems are respectively
obtained via a unified approach for the first time. Several new interesting
facts arise in mean-variance problems with constant risk aversion. For example,
it is shown that equilibrium strategies are still allowed to rely on initial
wealth as long as risk-free return rate is random. In addition, the closed-loop
equilibrium strategy and open-loop equilibrium strategy have the same
connection with initial wealth in non-Markovian setting, and they happen to
equal to each other if only risk-free return rate is deterministic.
