标题： 基于潜在侧信息依赖结构的序列投资组合选择：最优性与通用学习算法 显示英文标题

标题： Sequential Portfolio Selection under Latent Side Information-Dependence Structure: Optimality and Universal Learning Algorithms

摘要： 本文研究了在一个资产价格之间存在潜在依赖结构且部分不可观测的侧信息的市场中构建最优无卖空顺序投资组合策略的投资问题，该侧信息通常是高维的。 结果显示，基于完美了解依赖结构和全市场信息形成的投资组合的动态策略，可能不会以无穷多次比保持时间不变的常数策略以更高的速率增长。 具体而言，如果市场是平稳的，这意味着依赖结构在统计上是稳定的，那么利用整个市场信息最大能力的最优动态策略的增长率几乎肯定会随着时间衰减到一个平衡状态，并渐近收敛到常数策略的增长率。 从技术角度来看，这项工作重新评估了普遍认为当市场过程独立同分布时，常数策略才能达到动态策略的最优极限增长率这一观点。 通过分析带有侧信息的平稳市场中的动态对数最优投资组合策略作为最优基准，我们表明即使动态策略不存在极限增长率的情况下，也几乎肯定存在一个随机最优常数策略。 因此，讨论了两种用于投资组合构建的学习算法方法，展示了在学习过程中移除侧信息的安全性，同时仍能保证渐近增长率与最优动态策略相当。 显示英文摘要

摘要： This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often high-dimensional. The results demonstrate that a dynamic strategy, which forms a portfolio based on perfect knowledge of the dependence structure and full market information over time, may not grow at a higher rate infinitely often than a constant strategy, which remains invariant over time. Specifically, if the market is stationary, implying that the dependence structure is statistically stable, the growth rate of an optimal dynamic strategy, utilizing the maximum capacity of the entire market information, almost surely decays over time into an equilibrium state, asymptotically converging to the growth rate of a constant strategy. Technically, this work reassesses the common belief that a constant strategy only attains the optimal limiting growth rate of dynamic strategies when the market process is identically and independently distributed. By analyzing the dynamic log-optimal portfolio strategy as the optimal benchmark in a stationary market with side information, we show that a random optimal constant strategy almost surely exists, even when a limiting growth rate for the dynamic strategy does not. Consequently, two approaches to learning algorithms for portfolio construction are discussed, demonstrating the safety of removing side information from the learning process while still guaranteeing an asymptotic growth rate comparable to that of the optimal dynamic strategy.