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A dual characterization of self-generation and exponential forward performances

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Gordan \v{Z}itkovi\'c
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.

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File URL: http://arxiv.org/abs/0809.0739
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0809.0739.

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Date of creation: Sep 2008
Date of revision: Dec 2009
Publication status: Published in Annals of Applied Probability 2009, Vol. 19, No. 6, 2176-2210
Handle: RePEc:arx:papers:0809.0739

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  1. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July. [Downloadable!] (restricted)
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