A dual characterization of self-generation and exponential forward performances

Gordan \v{Z}itkovi\'c

Papers from arXiv.org

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.

Date: 2008-09, Revised 2009-12
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Citations: View citations in EconPapers (8)

Published in Annals of Applied Probability 2009, Vol. 19, No. 6, 2176-2210

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0809.0739

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