A dual characterization of self-generation and exponential forward performances

42Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

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 Itô-processes, where we obtain an explicit parametrization of all exponential forward performances. © Institute of Mathematical Statistics, 2009.

Cite

CITATION STYLE

APA

Žitkovic, G. (2009). A dual characterization of self-generation and exponential forward performances. Annals of Applied Probability, 19(6), 2176–2210. https://doi.org/10.1214/09-AAP607

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free