标题： 基于随机交易成本的功能生成投资组合：理论与实证证据 显示英文标题

标题： Functionally Generated Portfolios Under Stochastic Transaction Costs: Theory and Empirical Evidence

摘要： 假设无摩擦交易，经典随机投资组合理论（SPT）提供了相对套利策略。 然而，现实执行中的成本是状态依赖的、波动的，并在流动性冲击期间承受越来越大的压力。 使用可能与资产价格相关的伊藤扩散过程，我们将SPT扩展到具有比例随机交易成本的连续时间股权市场。 我们推导出一大类功能生成投资组合的成本调整相对财富的显式下界；这些下界为相对套利在随机成本下生存提供了充分条件。 结合限价订单簿成本代理和米尔斯汀方案验证了理论的数量级估计。 最后，我们在CRSP小盘股数据（1994--2024）的回测中使用日内买卖价差作为成本波动的替代指标。 尽管在2008年和2020年的流动性危机中经历了更大的下跌，但多样化和熵加权投资组合在扣除成本后，分别以每年3.6和2.9个百分点的优势超越市值加权基准。 显示英文摘要

摘要： Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during liquidity shocks. Using an Ito diffusion that may be connected with asset prices, we extend SPT to a continuous-time equity market with proportional, stochastic transaction costs. We derive closed-form lower bounds on cost-adjusted relative wealth for a large class of functionally generated portfolios; these bounds provide sufficient conditions for relative arbitrage to survive random costs. A limit-order-book cost proxy in conjunction with a Milstein scheme validates the theoretical order-of-magnitude estimates. Finally, we use intraday bid-ask spreads as a stand-in for cost volatility in a back-test of CRSP small-cap data (1994--2024). Despite experiencing larger declines during the 2008 and 2020 liquidity crises, diversity- and entropy-weighted portfolios continue to beat the value-weighted benchmark by 3.6 and 2.9 percentage points annually, respectively, after cost deduction.