Some Functional Equations Connected with the Utility of Gains and Losses - Titioura, Andrei (University of Waterloo, 2002)
The behavioral properties shown by people when they make selections between different choices will be studied. Based on empirical and logical data a mathematical axiomatic model is built. D. Luce is a major contributor in this area. This thesis is based on his works and those of his many co-authors. Three approaches will be considered that lead to the rank-dependent utility representation of binary gambles composed only of gains (losses) relative to a status quo. The proofs involve the theory of functional equations which is a very powerful tool giving the precise numerical representations.
Keywords: Mathematics; Utility; functional equations; binary gambles; RDU representation