Trading strategies generated by Lyapunov functions

Abstract

Functional portfolio generation, initiated by E.R. Fernholz almost 20 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, and needs no estimation of model parameters. In this paper, the corresponding generating functions G are interpreted as Lyapunov functions for the vector process μ of relative market weights; that is, via the property that the process G(μ) is a supermartingale under an appropriate change of measure. This point of view unifies, generalizes, and simplifies many 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 approach offered here yields results concerning the interplay of stochastic discount factors and concave transformations of semimartingales on compact domains.