Trading strategies generated pathwise by functions of market weights

Ioannis Karatzas () and Donghan Kim ()
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Ioannis Karatzas: Columbia University
Donghan Kim: Columbia University

Finance and Stochastics, 2020, vol. 24, issue 2, No 6, 423-463

Abstract: Abstract 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.

Keywords: Stochastic portfolio theory; Pathwise Itô and Tanaka formulas; Trading strategies; Functional generation; Strong relative arbitrage; 60G48; 60H05; 91G10 (search for similar items in EconPapers)
JEL-codes: D52 D53 G12 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00780-019-00414-2

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