AI 中文总结
在无概率考虑的路径设定下发展投资组合理论，用趋势提取器等分解取代半鞅分解，运用路径版伊藤积分，得出增长计价和可行性有界性等价关系，与半鞅对应关系有相似但也有分离，通过例子说明。
AI 中文摘要
投资组合理论及其相关概念和关于增长最优性、计价属性和“市场可行性”（排除了以任意小的初始资本为起点为非平凡未来负债流融资的可能性）的基本结果，是在完全没有概率考虑的路径设定中发展起来的。该方法用通过合适的趋势提取器及其相关残差路径生成的分解，取代了资产回报的随机分析中熟悉的半鞅分解；然后运用了福尔默著名的经典伊藤积分和微积分的路径版本。由此产生的增长计价和可行性有界性等价关系与它们的半鞅对应关系有相当大的相似性，但在路径设定中不一定会合并为一个等价类；通过两个例子说明了这种分离。
英文摘要
The theory of portfolios, and its allied notions and fundamental results concerning growth optimality, the numéraire property, and ``market viability'' -- which rules out the possibility of financing nontrivial future liability streams starting with arbitrarily small initial capital -- is developed in a pathwise setting, completely devoid of probabilistic considerations. The approach replaces the familiar semimartingale decomposition of stochastic analysis for assets' returns, by decompositions generated through suitable trend extractors and their associated residual paths; then deploys Föllmer's celebrated pathwise version of classical Itô integration and calculus. The resulting growth-numéraire and viability-boundedness equivalences bear considerable similarities to their semimartingale counterparts, but need not collapse into a single equivalence class in the pathwise setting; this separation is illustrated by two examples.
