Hindawi Publishing Corporation Advances in Decision Sciences Volume 2010, Article ID 302895, 8 pages doi:10.1155/2010/302895 Research Article Segregation and Integration: A Study of the Behaviors of Investors with Extended Value Functions Martin Egozcue 1 and Wing-Keung Wong 2 1 Department of Economics, University of Montevideo, Uruguay 2 Department of Economics, Hong Kong Baptist University, Hong Kong Correspondence should be addressed to Wing-Keung Wong, awong@hkbu.edu.hk Received 26 March 2010; Accepted 24 May 2010 Academic Editor: Chenghu Ma Copyright q 2010 M. Egozcue and W.-K. Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper extends prospect theory, mental accounting, and the hedonic editing model by developing an analytical theory to explain the behavior of investors with extended value functions in segregating or integrating multiple outcomes when evaluating mental accounting. 1. Introduction and Literature Review 1.1. Prospect Theory and Mental Accounting A central tenet within economics is that individuals maximize their expected utilities 1 in which all outcomes are assumed to be integrated with current wealth. Kahneman and Tversky 2 propose prospect theory to reflect the subjective desirability of different decision outcomes and to provide possible explanations for behavior of investors who maximize over value functions instead of utility functions. Let R be the set of extended real numbers and Ωa, b ⊂ R in which a< 0 and b> 0. Rather than defining over levels of wealth, the value function v is defined over gains and losses relative to a reference point status quo x o ∈ Ω with a<x o <b, satisfying -1 i v i x ≤ 0 for any x ∈ x o ,b, and v i ≥ 0 for any x ∈ a, x o , i 1, 2, 1.1 where v i x is the ith derivative of v. The value function is a psychophysical function to reflect the anticipated happiness or sadness associated with each potential decision outcome. Without loss of generality, we