The Annals of Applied Probability

A dual characterization of self-generation and exponential forward performances

Gordan Žitković

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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.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 6 (2009), 2176-2210.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1259158770

Digital Object Identifier
doi:10.1214/09-AAP607

Mathematical Reviews number (MathSciNet)
MR2588243

Zentralblatt MATH identifier
1180.91129

Subjects
Primary: 91B16: Utility theory
Secondary: 91B28

Keywords
Exponential utility forward performances incomplete markets utility maximization convex duality random fields mathematical finance

Citation

Žitković, Gordan. A dual characterization of self-generation and exponential forward performances. Ann. Appl. Probab. 19 (2009), no. 6, 2176--2210. doi:10.1214/09-AAP607. https://projecteuclid.org/euclid.aoap/1259158770


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