Twenty years ago, E.R. Fernholz introduced the notion of “functional generation” to construct a variety of portfolios solely in terms of the individual companies’ market weights. I. Karatzas and J. Ruf recently developed another approach to the functional construction of portfolios which leads to very simple conditions for strong relative arbitrage with respect to the market. Here, both of these notions are generalized in a pathwise, probability-free setting; portfolio-generating functions, possibly less smooth than twice differentiable, involve the current market weights as well as additional bounded-variation functionals of past and present market weights. This leads to a wider class of functionally generated portfolios than was heretofore possible to analyze, to novel methods for dealing with the “size” and “momentum” effects, and to improved conditions for outperforming the market portfolio over suitable time horizons.

中文翻译：

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通过市场权重函数逐步生成的交易策略

二十年前，ER Fernholz引入了“功能生成”的概念，仅根据各个公司的市场权重来构建各种投资组合。I. Karatzas和J. Ruf最近开发了另一种方法来构建投资组合的功能，这导致了非常简单的条件来针对市场进行强势相对套利。在这里，这两个概念都是以无风险的无路径方式概括的。投资组合生成函数可能不如两次可微划分的平滑，它涉及当前市场权重以及过去和现在市场权重的其他有界变化函数。这导致了功能生成的投资组合的类别比以前所能分析的要广泛，从而产生了处理“规模”和“动量”效应的新颖方法，