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Trading strategies generated by Lyapunov functions

Karatzas, Ioannis and Ruf, Johannes (2017) Trading strategies generated by Lyapunov functions. Finance and Stochastics. ISSN 0949-2984

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Identification Number: 10.1007/s00780-017-0332-8


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.

Item Type: Article
Official URL:
Additional Information: © 2017 The Authors © CC BY 4.0
Divisions: Mathematics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Date Deposited: 01 Feb 2017 15:24
Last Modified: 20 Sep 2021 01:49

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