Admissible Strategies in Semimartingale Portfolio Selection

Sara Biagini and Ale\v{s} \v{C}ern\'y
Authors registered in the RePEc Author Service: Aleš Černý

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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 (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.

Date: 2009-10, Revised 2010-12
New Economics Papers: this item is included in nep-upt
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Published in SIAM J. Control Optim. 49(1) (2011) 42-72

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Working Paper: Admissible strategies in semimartingale portfolio selection (2010)
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