This paper investigates a continuous-time mean-variance portfolio selection problem based on a log-return model. The financial market is composed of one risk-free asset and multiple risky assets whose prices are modelled by geometric Brownian motions. We derive a sufficient condition for open-loop equilibrium strategies via forward backward stochastic differential equations (FBSDEs). An equilibrium strategy is derived by solving the system. To illustrate our result, we consider a special case where the interest rate process is described by the Vasicek model. In this case, we also derive the closed-loop equilibrium strategy through the dynamic programming approach.

中文翻译：

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选择均值方差投资组合的开环均衡策略：对数收益模型

本文研究了基于对数收益模型的连续时间均方差投资组合选择问题。金融市场由一种无风险资产和多种风险资产组成，其价格由几何布朗运动模拟。通过前向后向随机微分方程（FBSDE），我们得出了开环平衡策略的充分条件。通过求解系统得出平衡策略。为了说明我们的结果，我们考虑一种特殊情况，其中通过Vasicek模型描述利率过程。在这种情况下，我们还通过动态规划方法得出了闭环平衡策略。