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A characterization of forward utility functions

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Recently, a notion of dynamically consistent utility functions has appeared in the mathematical finance literature, under the name forward dynamic utility functions in the work of Musiela and Zariphopoulou and as horizon-unbiased utility functions in that of Henderson and Hobson. Working in a fairly general (possibly incomplete) market with continuous asset prices, we present representations of all forward utility functions in terms of their convex conjugate functions. This is joint work with Chris Rogers and Francois Berrier.

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