Optimal Investments for Robust Utility Functionals in Complete Market Models

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...

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Veröffentlicht in:Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 30(2005), 3, Seite 750-764
1. Verfasser: Schied, Alexander (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2005
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... Secondary: probability: stochastic model applications Mathematics Economics Applied sciences
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520 |a 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 of probability measures. Our main result shows that this problem can often be reduced to determining a "least favorable" measure Q₀ ∈ , 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 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." 
540 |a Copyright 2005 Institute for Operations Research and the Management Sciences 
650 4 |a Robust utility functional 
650 4 |a Utility maximization 
650 4 |a Knightian uncertainty 
650 4 |a Robust Savage representation 
650 4 |a Least favorable measure 
650 4 |a Uncertain drift 
650 4 |a Huber-Strassen theory 
650 4 |a Primary 91B28 
650 4 |a Secondary 60G44 
650 4 |a Primary: Utility/preference: applications 
650 4 |a Secondary: probability: stochastic model applications 
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650 4 |a Economics  |x Microeconomics  |x Economic utility  |x Utility functions 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions  |x Monotonic functions  |x Decreasing functions 
650 4 |a Economics  |x Microeconomics  |x Economic utility  |x Expected utility 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical theorems 
650 4 |a Economics  |x Economic disciplines  |x Financial economics  |x Finance  |x Financial investments 
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650 4 |a Economics  |x Microeconomics  |x Economic utility  |x Expected utility 
655 4 |a research-article 
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