Economy – Quantitative Finance – Computational Finance
Scientific paper
2009-10-20
SIAM J. Control Optim. 49 (2002) 42-72
Economy
Quantitative Finance
Computational Finance
30 pages
Scientific paper
10.1137/090774458
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.
Biagini Sara
Černý Aleš
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