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

Mean-variance portfolio selection and variance hedging with random coefficients: closed-loop equilibrium strategy