Admissible strategies in semimartingale portfolio selection

Biagini, S. & Černý, A. (2011). Admissible strategies in semimartingale portfolio selection. SIAM Journal on Control and Optimization, 49(1), pp. 42-72. doi: 10.1137/090774458

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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.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Technology, Physical Sciences, Automation & Control Systems, Mathematics, Applied, Mathematics, AUTOMATION & CONTROL SYSTEMS, MATHEMATICS, APPLIED, utility maximization, nonlocally bounded semimartingale, incomplete market, sigma-localization and I-localization, sigma-martingale measure, Orlicz space, convex duality, EXPONENTIAL UTILITY MAXIMIZATION, INCOMPLETE MARKETS, OPTIMAL INVESTMENT, MARTINGALES, PROPERTY, WEALTH, CLAIMS
Subjects: H Social Sciences > HG Finance
Divisions: Cass Business School > Faculty of Finance
URI: http://openaccess.city.ac.uk/id/eprint/3255

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