Trading Strategies Generated by Lyapunov Functions

TL;DR

This paper introduces a novel approach to constructing trading strategies using Lyapunov functions, unifying and simplifying existing methods while providing conditions for outperforming the market portfolio.

Contribution

It interprets generating functions as Lyapunov functions for market weights, generalizing previous results and establishing new conditions for market outperformance.

Findings

Unifies existing portfolio generation methods with Lyapunov functions.

Provides conditions for outperforming the market portfolio.

Analyzes stochastic discount factors and semimartingales on compact domains.

Abstract

Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameters. In this paper, the corresponding generating functions $G$ are interpreted as Lyapunov functions for the vector process $\mu(\cdot)$ of market weights; that is, via the property that $G(\mu(\cdot))$ is a supermartingale under an appropriate change of measure. This point of view unifies, generalizes, and simplifies several existing results, and allows the formulation of conditions under which it is possible to outperform the market portfolio over appropriate time-horizons. From a probabilistic point of view, the present paper yields results concerning the interplay of stochastic discount factors and concave transformations of semimartingales on compact domains.