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Alexander Schied, Ching-Tang Wu
Duality theory for optimal investments under model uncertainty
Keywords: portfolio optimization, model uncertainty, Knightian uncertainty, coherent risk measures, convex duality
Robust utility functionals arise as numerical representations of investor preferences, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In this paper, we study the duality theory for the problem of maximizing the robust utility of the terminal wealth in a general incomplete market model. We also allow for very general sets of prior models. In particular, we do not assume that all prior models are equivalent to each other, which allows us to handle many economically meaningful robust utility functionals such as those defined by AVaRλ, concave distortions, or convex capacities. We also show that dropping the equivalence of prior models may lead to new effects such as the existence of arbitrage strategies under the least favorable model.
Statistics & Decisions, Oldenbourg Wissenschaftsverlag
Print ISSN: 0721-2631
Volume: 23, 03/2005
Pages: 199 - 217