Admissible Strategies in Semimartingale Portfolio Selection

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.

30 pages

References in corpus (2)

• On the Structure of General Mean-Variance Hedging Strategies
• On the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets

Cited by in corpus (5)

• Convex duality and Orlicz spaces in expected utility maximization
• Semimartingale theory of monotone mean--variance portfolio allocation
• Simplified stochastic calculus with applications in Economics and Finance
• On Admissible Strategies in Robust Utility Maximization
• Dynamically optimal portfolios for monotone mean--variance preferences