A dual characterization of self-generation and exponential forward performances
Abstract
We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal one reflects a Nisio-type semigroup property, referred to as self-generation. In the setting of semimartingale financial markets, we provide a dual formulation of self-generation in addition to the original one, and show equivalence between the two, thus giving a dual characterization of forward performances. Then we focus on random fields with an exponential structure and provide necessary and sufficient conditions for self-generation in that case. Finally, we illustrate our methods in financial markets driven by It\^o-processes, where we obtain an explicit parametrization of all exponential forward performances.
Keywords
Cite
@article{arxiv.0809.0739,
title = {A dual characterization of self-generation and exponential forward performances},
author = {Gordan Žitković},
journal= {arXiv preprint arXiv:0809.0739},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/09-AAP607 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)