  The choice of admissible trading strategies in mathematical modelling of
financial markets is a delicate issue, going back to Harrison and Kreps (1979).
In the context of optimal portfolio selection with expected utility preferences
this question has been a focus of considerable attention over the last twenty
years. We propose a novel notion of admissibility that has many pleasant
features - admissibility is characterized purely under the objective measure;
each admissible strategy can be approximated by simple strategies using finite
number of trading dates; the wealth of any admissible strategy is a
supermartingale under all pricing measures; local boundedness of the price
process is not required; neither strict monotonicity, strict concavity nor
differentiability of the utility function are necessary; the definition
encompasses both the classical mean-variance preferences and the monotone
expected utility. For utility functions finite on the whole real line, our
class represents a minimal set containing simple strategies which also contains
the optimizer, under conditions that are milder than the celebrated reasonable
asymptotic elasticity condition on the utility function.
