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Abstract: We propose a mathematical framework for the study of a family of randomfields-called forward performances-which arise as numerical representation ofcertain rational preference relations in mathematical finance. Their spatialstructure corresponds to that of utility functions, while the temporal onereflects a Nisio-type semigroup property, referred to as self-generation. Inthe setting of semimartingale financial markets, we provide a dual formulationof self-generation in addition to the original one, and show equivalencebetween the two, thus giving a dual characterization of forward performances.Then we focus on random fields with an exponential structure and providenecessary and sufficient conditions for self-generation in that case. Finally,we illustrate our methods in financial markets driven by It\^o-processes, wherewe obtain an explicit parametrization of all exponential forward performances.



Author: Gordan Žitković

Source: https://arxiv.org/







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