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Admissible strategies in semimartingale portfolio selection

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  • Sara Biagini
  • Ales Cerny
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    Abstract

    The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps [HK79]. In the context of optimal portfolio selection with expected utility preferences this question has been the 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 P; 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 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.

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    File URL: http://www.carloalberto.org/assets/working-papers/no.117.pdf
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    Bibliographic Info

    Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 117.

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    Length: 35 pages
    Date of creation: 2009
    Date of revision: 2010
    Handle: RePEc:cca:wpaper:117

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    Related research

    Keywords: utility maximization; non locally bounded semimartingale; incomplete market; sigma-localization and I-localization; sigma-martingale measure; Orlicz space; convex duality;

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