Admissible strategies in semimartingale portfolio selection

Sara Biagini and Aleš Černý

No 117, Carlo Alberto Notebooks from Collegio Carlo Alberto

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.

Keywords: utility maximization; non locally bounded semimartingale; incomplete market; sigma-localization and I-localization; sigma-martingale measure; Orlicz space; convex duality (search for similar items in EconPapers)
JEL-codes: G11 G12 G13 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2009, Revised 2010
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Related works:
Working Paper: Admissible Strategies in Semimartingale Portfolio Selection (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:cca:wpaper:117

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