Optimal Investments for Robust Utility Functionals in Complete Market Models
This paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set 𝒬 of probability measures. Our main result shows that this problem...
| Veröffentlicht in: | Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 30(2005), 3, Seite 750-764 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2005
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| Zugriff auf das übergeordnete Werk: | Mathematics of Operations Research |
| Schlagworte: | Robust utility functional Utility maximization Knightian uncertainty Robust Savage representation Least favorable measure Uncertain drift Huber-Strassen theory Primary 91B28 Secondary 60G44 Primary: Utility/preference: applications mehr... |
| Zusammenfassung: | This paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set 𝒬 of probability measures. Our main result shows that this problem can often be reduced to determining a "least favorable" measure Q₀ ∈ 𝒬, which is universal in the sense that it does not depend on the particular utility function. The robust problem is thus equivalent to a standard utility-maximization problem with respect to the "subjective" probability measure Q₀. By using the Huber-Strassen theorem from robust statistics, it is shown that Q₀ always exists if 𝒬 is the σ-core of a 2-alternating capacity. Besides other examples, we also discuss the problem of robust utility maximization with uncertain drift in a Black-Scholes market and the case of "weak information." |
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| ISSN: | 15265471 |