发表机构
National Institute of Technology Sikkim; Montana Technological University; George Washington University（锡金国立理工学院; 蒙大拿理工大学; 乔治华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于Mixup条形码和持续同调的拓扑感知金融决策系统，结合拓扑摘要与压力评分动态调整黄金交叉交易法，在S&P 500和比特币上取得优于基准的夏普比率与更低回撤。
AI 中文摘要
我们提出了一种基于Mixup条形码和持续同调的拓扑感知金融决策系统。该方法使用从单变量价格序列的Takens延迟嵌入中获得的拓扑摘要，量化参考市场 regime 与当前市场 regime 之间的结构变化。结合持续图之间的1- Wasserstein距离、Mixup条形码干扰指数和持续熵散度，得到一种新型压力评分。该评分动态调整黄金交叉（Golden Cross）交易方法，将二元买入/卖出信号转化为连续的头寸规模调整过程。在72点网格上最大化样本内夏普比率（Sharpe）所选的嵌入设置下，对标准普尔500（S&P 500）和比特币的样本内评估分别得到1.116和1.238的夏普比率，与买入并持有策略和标准黄金交叉基线相比，最大回撤显著更低。我们的发现表明，市场几何的拓扑摘要包含超出传统趋势指标的有用信息。
英文摘要
We present a topology-aware system based on mixup barcodes and persistent homology for financial decision making. The suggested approach uses topological summaries obtained from Takens delay embeddings of a univariate price series to quantify structural changes between reference and current market regimes. The 1-Wasserstein distance between persistence diagrams, a mixup barcode disruption index, and persistence entropy divergence are combined to provide a novel stress score. A Golden Cross trading method is dynamically modulated by this score, which transforms a binary buy/sell signal into a continuous position-sizing process. At embedding settings chosen by maximizing in-sample Sharpe over a 72-point grid, in-sample assessment on the S&P 500 and Bitcoin yields Sharpe ratios of 1.116 and 1.238, respectively, with much lower maximum drawdown compared with both Buy-and-Hold and the standard Golden Cross baseline. Our findings imply that topological summaries of market geometry include useful information that goes beyond traditional trend markers.
Comments22 pages, 7 figures, 2 tables
