论文标题
沃斯坦舞会中的投资组合优化
Portfolio Optimisation within a Wasserstein Ball
论文作者
论文摘要
我们研究了主动投资组合管理的问题，在该问题中，投资者的目标是超越基准策略的风险概况，同时又不偏离它。具体而言，投资者考虑了替代策略，其终端财富位于围绕基准的瓦斯坦巨星中 - 分配在分配上很近 - 并且具有指定的依赖/copula - 与国家逐个状态相关联。然后，投资者选择了替代策略，以最大程度地减少终极财富的失真风险度量。在一般（完整）的市场模型中，我们证明存在最佳的动态策略，并通过等渗预测的概念提供了表征。 我们进一步提出了一种模拟方法来计算最佳策略的终端财富，使我们的方法适用于广泛的市场模型。最后，我们说明了使用不同的偏好和风险偏好的投资者如何使用尾巴的风险，反向S形和下尾扭曲风险措施来投资和改进基准。我们发现，投资者的最佳终端财富分布在区域中具有更大的概率质量，这些区域降低了相对于基准的风险度量，同时保留了基准的结构。
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth. In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections. We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure.
