Empirical_Portfolio
通过概率经验回报分布估计和混合整数线性规划的均值-VaR投资组合优化
在此存储库中的Jupyter笔记本（.ipynb）中，我们提供了一种流行的现代投资组合理论（MPT）方法的替代方法，以优化资产分配。 与MPT相反，在MPT中，财务风险是通过预测收益的波动性（即标准误）来建模的，我们选择通过预测收益的经验性联合分布并制定优化问题以选择资产的目的，来更明确地表征此风险。分配以最大化该分布的均值，并限制资产选择的选择，以确保不会违反根据此经验分布测得的某些风险值（VaR）。 这种方法的主要原因是要解决MPT的主要缺点之一，即不一定捕获回报分配中可能很重的尾巴的行为，从而低估了资产的实际风险。
总体方法可以总结如下：
我们基于历史资产收益建立时间序列模型，以使模型的残差独立且均匀地分布（iid）。 我们使用模型和残差来生成自举预测，即使用时间序列模型预测下一个返回值，并从iid残差中随机采
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