标题： 长期投资中超越最佳常数再平衡组合：对Kelly准则的推广以及适用于序列依赖市场的通用学习算法 显示英文标题

标题： Beating the Best Constant Rebalancing Portfolio in Long-Term Investment: A Generalization of the Kelly Criterion and Universal Learning Algorithm for Markets with Serial Dependence

摘要： 在在线投资组合优化框架中，现有的学习算法生成的策略在累积财富方面与事后最佳恒定再平衡投资组合相比显著较差，尽管它们在渐近增长速率上是一致的。 虽然通过引入更多辅助信息可以改善这种不理想的表现，但这在特征选择和高维设置中带来了困难。 相反，资产收益的固有时间依赖性，如星期几和其他日历效应，可以被利用。 尽管使用大型训练数据集通常可以检测到潜在的时间依赖模式，但本文提出了一种算法，仅使用逐步揭示的数据来学习这种依赖关系，而无需对其分布做出任何假设，从而形成一种最终超过最佳恒定再平衡投资组合累积财富的策略。 此外，经典的凯利准则要求资产收益是独立的，在一个作为独立同分布随机矩阵过程建模的市场中，该准则被推广以适应时间依赖性。 在这种现有为平稳过程设计的学习算法无法适用的随机市场中，所提出的算法仍然生成一种渐近增长到所有策略中最高速率的策略，与在广义凯利准则下构建的最优策略相匹配。 使用真实市场数据的实验结果证明了该算法的理论保证及其预期性能，只要时间依赖性显著，无论广义凯利准则在实验市场中是否有效。 这进一步证实了该算法在一般情境中的广泛应用性。 显示英文摘要

摘要： In the online portfolio optimization framework, existing learning algorithms generate strategies that yield significantly poorer cumulative wealth compared to the best constant rebalancing portfolio in hindsight, despite being consistent in asymptotic growth rate. While this unappealing performance can be improved by incorporating more side information, it raises difficulties in feature selection and high-dimensional settings. Instead, the inherent serial dependence of assets' returns, such as day-of-the-week and other calendar effects, can be leveraged. Although latent serial dependence patterns are commonly detected using large training datasets, this paper proposes an algorithm that learns such dependence using only gradually revealed data, without any assumption on their distribution, to form a strategy that eventually exceeds the cumulative wealth of the best constant rebalancing portfolio. Moreover, the classical Kelly criterion, which requires independent assets' returns, is generalized to accommodate serial dependence in a market modeled as an independent and identically distributed process of random matrices. In such a stochastic market, where existing learning algorithms designed for stationary processes fail to apply, the proposed learning algorithm still generates a strategy that asymptotically grows to the highest rate among all strategies, matching that of the optimal strategy constructed under the generalized Kelly criterion. The experimental results with real market data demonstrate the theoretical guarantees of the algorithm and its performance as expected, as long as serial dependence is significant, regardless of the validity of the generalized Kelly criterion in the experimental market. This further affirms the broad applicability of the algorithm in general contexts.