Non-Markovian Mean-Variance Portfolio Selection Problems via Closed-Loop Equilibrium Strategies

In this article, a class of mean-variance portfolio selection problems with constant risk aversion is investigated by means of closed-loop equilibrium strategies. Thanks to the non-Markovian setting, two delicate kinds of equilibrium strategies are introduced and both of them obviously reduce to the existing counterpart in the Markovian case. To explicitly represent the equilibrium strategy, a class of backward stochastic Riccati system is introduced, and its solvability is carefully discussed for the first time in the literature. Different from the current literature, the spectacular role of random interest rates in the model is firstly indicated by several interesting phenomena, and the new deeper relations between closed-loop, open-loop equilibrium strategies are shown as well. Finally, numerical analysis via deep learning method is shown to illustrate the novel theoretical findings.