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On a Class of Multiattribute Utility Functions Invariant under Shift Transformations

100%
Chudziak J.
|
|
issue 4
673-675
EN
We consider a class of multiattribute utility functions which are invariant with respect to the shifts having identical parameters for each attribute.
2
Content available remote

Utility Functions Invariant with Respect to Some Classes of Shifts

100%
Chudziak J.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
508-512
EN
A utility function U is said to be invariant with respect to a family of transformations Γp provided, for every member γ of Γp, U and Uırc γ represent the same preference relation over lotteries. An invariance with respect to a wide class of transformations can be reduced to an invariance with respect to the shift transformations. We give a complete answer to the following question: given a nonempty set T of shifts determine all utility functions invariant with respect to the shift transformations by every element of T. As a consequence of our results we obtain the forms of utility functions invariant with respect to the families of commuting transformations.
3
Content available remote

On a Class of One-Switch Multiattribute Utility Functions

100%
Chudziak J.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-11-B-15
EN
We determine the functional forms of a class of multiattribute utility functions that lead to zero-switch change in preferences between multi-period cash flows when a decision maker's initial wealth increases through an annuity that pays a constant amount every time period.
4
Content available remote

On the Foster-Hart Measure of Riskiness under Cumulative Prospect Theory

63%
Chudziak J., Halicki M.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
950-954
EN
We prove the existence of the Foster-Hart measure of riskiness under the cumulative prospect theory and we study some of its basic properties.
5
Content available remote

Scale Invariance of Principle of Equivalent Utility under Cumulative Prospect Theory

51%
Chudziak J., Halicki M., Wójcik S.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-29-A-32
EN
In 1984 A. Reich proved that under Expected Utility Theory, a scale invariance of the Principle of Equivalent Utility just for two particular values of parameters implies its scale invariance. In this paper, we extend this result onto the Principle of Equivalent Utility under Cumulative Prospect Theory.
6
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Positive Homogeneity of the Principle of Equivalent Utility

51%
Chudziak J., Chudziak M., Sobek B.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
941-944
EN
We prove that if the principle of equivalent utility under the cumulative prospect theory is positively homogeneous on a relatively small family of risks for every non-negative initial wealth level, then a value function is linear for gains and losses, but, in general, it needs not be linear.
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