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Admissible Strategies in Semimartingale Portfolio Selection

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  • Sara Biagini
  • Alev{s} v{C}ern'y

Abstract

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.

Suggested Citation

  • Sara Biagini & Alev{s} v{C}ern'y, 2009. "Admissible Strategies in Semimartingale Portfolio Selection," Papers 0910.3936, arXiv.org, revised Dec 2010.
  • Handle: RePEc:arx:papers:0910.3936
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