带Choquet正则化项的探索性均值-方差投资组合选择
Exploratory mean-variance portfolio selection with Choquet regularizers
AI总结：
本文在强化学习框架下研究连续时间探索性均值-方差投资组合问题，利用Choquet正则化项刻画探索水平，显式求解最优分布并设计强化学习算法比较不同正则化形式的效果。
摘要：
本文在强化学习框架下研究连续时间探索性均值-方差问题，并采用Choquet正则化项来衡量探索水平。通过应用经典Bellman最优性原理，推导出该探索性均值-方差问题的Hamilton-Jacobi-Bellman方程，并通过静态最大化一个受均值-方差约束的Choquet正则化项来显式求解。特别地，最优分布构成一个位置-尺度族，其形状取决于Choquet正则化项的选择。我们进一步利用Choquet正则化项的一个变体重新表述了连续时间Choquet正则化的探索性均值-方差问题。在特定的Choquet正则化项下给出了若干例子，这些正则化项生成了广泛使用的探索采样器，如指数分布、均匀分布和高斯分布。最后，我们设计了一个强化学习算法，以模拟并比较两种不同正则化形式下的结果。
英文摘要：
In this paper, we study a continuous-time exploratory mean-variance (EMV) problem under the framework of reinforcement learning (RL), and the Choquet regularizers are used to measure the level of exploration. By applying the classical Bellman principle of optimality, the Hamilton-Jacobi-Bellman equation of the EMV problem is derived and solved explicitly via maximizing statically a mean-variance constrained Choquet regularizer. In particular, the optimal distributions form a location-scale family, whose shape depends on the choices of the Choquet regularizer. We further reformulate the continuous-time Choquet-regularized EMV problem using a variant of the Choquet regularizer. Several examples are given under specific Choquet regularizers that generate broadly used exploratory samplers such as exponential, uniform and Gaussian. Finally, we design a RL algorithm to simulate and compare results under the two different forms of regularizers.
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