Admissible strategies in semimartingale portfolio selection

The choice of admissible trading strategies in mathematical modeling of financial markets is a delicate issue, going back to Harrison and Kreps. In the context of optimal portfolio selection with expected utility preferences this question has been the focus of considerable attention over the last 20 years. We propose a novel notion of admissibility that has many pleasant features—admissibility is characterized purely under the objective measure P; each admissible strategy can be approximated by simple strategies using a 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 is necessary; the definition encompasses both the classical mean-variance preferences and the monotone expected utility. For utility functions finite on R, 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.