Generalised Lyapunov Functions and Functionally Generated Trading Strategies

TL;DR

This paper explores how generalized Lyapunov functions can be used to develop and analyze functionally generated trading strategies, providing theoretical conditions for arbitrage and empirical validation with stock market data.

Contribution

It extends the theory of functional portfolio generation by incorporating an extra finite variation process and establishes conditions for strong arbitrage strategies.

Findings

Derived a general class of potential arbitrage strategies.

Provided empirical examples using S&P 500 data.

Formulated conditions for arbitrage relative to the market.

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 Komlos 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.