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Admissible Strategies in Semimartingale Portfolio Selection


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


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.

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

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    References listed on IDEAS

    1. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
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    3. Jung, Woo-Sung & Kwon, Okyu & Wang, Fengzhong & Kaizoji, Taisei & Moon, Hie-Tae & Stanley, H. Eugene, 2008. "Group dynamics of the Japanese market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 537-542.
    4. Sergei Maslov, 2001. "Measures of globalization based on cross-correlations of world financial indices," Papers cond-mat/0103397,, revised Apr 2001.
    5. Eryiğit, Mehmet & Eryiğit, Resul, 2009. "Network structure of cross-correlations among the world market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3551-3562.
    6. Maslov, Sergei, 2001. "Measures of globalization based on cross-correlations of world financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 397-406.
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