Generalised Lyapunov Functions and Functionally Generated Trading Strategies

Applied Mathematical Finance, 2020

28 Pages Posted: 17 Jul 2020

See all articles by Johannes Ruf

Johannes Ruf

London School of Economics & Political Science (LSE) - London School of Economics

Kangjianan Xie

Lloyds Banking Group

Date Written: June 25, 2020

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

Suggested Citation

Ruf, Johannes and Xie, Kangjianan, Generalised Lyapunov Functions and Functionally Generated Trading Strategies (June 25, 2020). Applied Mathematical Finance, 2020, Available at SSRN: https://ssrn.com/abstract=3635641

Johannes Ruf

London School of Economics & Political Science (LSE) - London School of Economics ( email )

United Kingdom

Kangjianan Xie (Contact Author)

Lloyds Banking Group ( email )

10 Gresham Street
London, EC2V 7AE
United Kingdom

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