Generalised Lyapunov Functions and Functionally Generated Trading Strategies

Abstract

This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies to be strong arbitrage relative to the market over sufficiently large time horizons. A mollification argument and Komlo's theorem yield a general class of potential arbitrage strategies. These theoretical results are complemented by several empirical examples using data from the S&P 500 stocks.

Keywords: Additive generation, Lyapunov function, market diversity, multiplicative generation, portfolio analysis, portfolio generating function, S&P 500, Stochastic Portfolio Theory

JEL Classification: G11