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.
CITATION STYLE
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
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