Trading strategies generated by Lyapunov functions

Ioannis Karatzas and Johannes Ruf

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 μ(⋅) of market weights; that is, via the property that G(μ(⋅)) 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.

Keywords: trading strategies; functional generation; relative arbitrage; regular and Lyapunov functions; concavity; semimartingale property; deflators (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2017-05-25
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (32)

Published in Finance and Stochastics, 25, May, 2017. ISSN: 0949-2984

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