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Multivariable Utility Functions
SIAM Journal on Optimization, 2009Utility functions of several variables are ubiquitous in economics. Their maximization requires inversion of the gradient map. Using convex analysis tools, we provide a representation of an extension of this inverse that accounts for possible constraints.
Maria B. Chiarolla, Ulrich G. Haussmann
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A Class of Utility Functions Containing all the Common Utility Functions
Management Science, 1987This paper presents a class of utility functions (class A∞) that contains all of the utility functions commonly used for mathematical modeling: the class consisting of those utility functions whose derivatives alternate in sign. A simple representation via mixtures of exponential utilities is provided for this class which is both mathematically ...
Patrick L. Brockett, Linda L. Golden
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Functional ANOVA, ultramodularity and monotonicity: Applications in multiattribute utility theory
European Journal of Operational Research, 2011 Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker's preference structure. These properties are usually characterized via partial derivatives.
Emanuele Borgonovo
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Multiplicative Utility Functions
Operations Research, 1974This paper presents sufficient conditions for a multiattribute utility function to be either multiplicative or additive. The number of requisite assumptions to imply the main result is equal to the number of attributes. Because the assumptions involve only trade-offs between two attributes at a time or lotteries over one attribute, it is reasonable to
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North American Actuarial Journal, 1998
This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility ...
Hans U. Gerber, Gérard Pafum
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This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility ...
Hans U. Gerber, Gérard Pafum
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Money-Metric Utility Functions
International Economic Review, 1985The paper considers a function \(M_ p(x)\) that specifies the minimum income needed at prices p to obtain a consumption vector preferred to x. This function is called a money metric. Sufficient conditions on the consumption set, on the preference relation, and on the prices are given ensuring that the money metric is a well-defined and continuous ...
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Double-Exponential Utility Functions
Mathematics of Operations Research, 1986Ordinal additivity between two attributes X and Y is a property that permits the utility function u(x, y) to be represented as ϕ(v(x) + w(y)) for some functions ϕ, v and w where ϕ may be thought of as a single attribute utility function over v + w. In applications ϕ is usually taken to be either linear (the additive decomposition) or exponential (the ...
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Synthese, 2003
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Utility as an Additive Set Function
Mathematics of Operations Research, 1992Foundations for additive models of subset evaluation are stated by axioms for a preference relation on a family S of subsets of X that cover X. The axiomatizations include cases in which S is arbitrary, S contains only finite subsets of X, and S is the set of all subsets of X. Expected utility with subsets as outcomes is also considered.
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Elicitation and utilization of application-level utility functions
Proceedings of the 6th international conference on Autonomic computing, 2009We present a non-analytic approach to self-assessment for Autonomic Computing. Our approach leverages utility functions, at the level of an autonomic application, or even a single task or feature being exercised within that application. This paper describes the fundamental steps of our approach: instrumentation of the application; collection of ...
Paul deGrandis, Giuseppe Valetto
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