发表机构
Sungshin Women’s University; KAIST（成均馆大学; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个基于价格的随机组合理论框架，通过名义价格权重生成策略并相对于价格加权基准评估，处理股票分割引起的跳跃，并证明提前调整信息无法保证改进性能，同时建立与资本化框架的对应关系并用NYSE数据验证。
AI 中文摘要
我们为随机组合理论开发了一个基于价格的框架，其中交易策略由名义价格权重生成，并相对于价格加权基准进行评估。股票分割和反向分割会在生成权重中引起跳跃，而不改变现有投资的价值。在具有可预测调整事件的半鞅市场中，我们将相应的股份调整纳入自融资条件，并构造具有显式跳跃修正财富分解的加性和乘性生成策略。对于加性生成，一个基于熵的示例表明，在重复分割下，相对财富几乎必然趋向于负无穷，这解释了为什么长期相对套利的通常论证不能直接扩展。我们还表明，仅凭提前调整信息并不能为功能生成组合提供无模型的性能改进保证。对于乘性生成，保持财富的重启保留了在当前价格权重下评估的经典组合配置。我们还建立了与基于资本化框架的对应关系，该框架保持绝对财富并产生与策略无关的基准转换。我们使用每日纽约证券交易所数据说明该框架，比较价格加权和资本化加权基准以及相应的多样性加权组合在价格和资本化选择的宇宙中的表现。
英文摘要
We develop a price-based framework for stochastic portfolio theory in which trading strategies are generated from nominal price weights and evaluated relative to a price-weighted benchmark. Stock splits and reverse splits induce jumps in the generating weights without changing the value of existing investments. In a semimartingale market with predictable adjustment events, we incorporate the corresponding share adjustments into the self-financing condition and construct additively and multiplicatively generated strategies with explicit jump-corrected wealth decompositions. For additive generation, an entropy-based example exhibits relative wealth tending to $-\infty$ almost surely under repeated splits, demonstrating why the usual argument for long-horizon relative arbitrage does not extend directly. We also show that advance adjustment information alone provides no model-free guarantee of improved performance for functionally generated portfolios. For multiplicative generation, wealth-preserving restarts retain the classical portfolio allocation evaluated at the current price weights. We also establish a correspondence with the capitalization-based framework that preserves absolute wealth and yields a strategy-independent benchmark conversion. We illustrate the framework using daily NYSE data, comparing price- and capitalization-weighted benchmarks and the corresponding diversity-weighted portfolios across price- and capitalization-selected universes.
Comments37 pages, 10 figures
