## One-switch utility functions with annuity payments

Jacek Chudziak

University of Rzeszow, Department of Mathematics, Al. Rejtana 16A, Rzeszów 35-959, Poland

 Abstract One of the most important steps in decision analysis is determining the decisions maker's utility function. Several authors have presented methods to derive the functional form of a utility function based on the change in valuation of a lottery as the decision maker's wealth increases. In particular, it is well known that if the decision maker's preferences between any two uncertain and uni-period lotteries does not change as the decision maker's initial wealth changes, then he must have either a linear or an exponential utility function. In 1988 D. Bell introduced the idea of characterizing a utility function based on the maximum number of switches that may occur between any two lotteries as the decision maker's  wealth increases.  It happens that in many cases that arise in practice, a decision maker may face multi-period and uncertain cash flows. In [1] and [2] we have derive the functional forms 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. In the present talk we investigate the functional forms of multiattribute utility functions that lead to a maximum of one-switch change in preferences. [1] A.E. Abbas, J. Aczel and J. Chudziak, Invariance of multiattribute utility functions under shift transformations, Result. Math. 54 (2009), 1-13. [2] J. Chudziak, On a class of multiattribute utility functions invariant under shift transformations, Acta Phys. Polon. A 117 (2010), 673-675.

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1. PRESENTATION: One-switch utility functions with annuity payments, PDF document, version 1.3, 0.2MB
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