Skip to content
All library documents

Functional Portfolio Generation with Generalised Lyapunov Functions

Article arXiv papers · Author: Johannes Ruf et al.
Read the original

Summary

The paper studies functionally generated portfolios and how their behavior changes when an additional finite variation process is included. It uses the framework of Karatzas and Ruf to formulate conditions under which a trading strategy can outperform the market with certainty over sufficiently long horizons, making it a strong arbitrage relative to the market.

The authors use mollification and Komlos's theorem to construct a broad class of candidate strategies with this property. They complement the theoretical development with empirical examples based on S&P 500 stocks. The supplied description does not specify the portfolio rules, sample period, benchmark details, or empirical results, so it does not establish how these strategies perform after transaction costs or in live trading. Its main contribution is a mathematical framework for identifying potential relative arbitrage, rather than a ready-to-deploy trading system.

Key ideas

  • Functionally generated portfolios can depend on an additional finite variation process.
  • The paper states conditions for strategies to be strong arbitrage relative to the market over sufficiently long horizons.
  • Mollification and Komlos's theorem are used to construct a broad class of potential arbitrage strategies.
  • Empirical examples use S&P 500 stocks, though the supplied description gives no performance details.

Tags

EquitiesPortfolio constructionArbitrageStatistics
Full text
# Generalised Lyapunov Functions and Functionally Generated Trading Strategies


# Generalised Lyapunov Functions and Functionally Generated Trading Strategies









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.