Segregation and Integration: A Study of the Behaviors of Investors with Extended Value Functions

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 be the set of extended real numbers and in which and . Rather than defining over levels of wealth, the value function is defined over gains and losses relative to a reference point (status quo) with , satisfying where is the derivative of . 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 assume the status quo to be zero. Thus, we refer to positive outcomes as gains and negative outcomes as losses. In this situation, investors with the value functions are risk averse for gains but risk seeking for losses. Since the value function is concave in the positive domain and convex for the negative domain, it shows declining sensitivity in both gains and losses. Kahneman [3] comments that evaluating an object from a reference point of “having” (“not having”) implies a negative (positive) change of “giving something up” (“getting something”) upon relinquishing (receiving) the object. Many functions have been proposed as value functions; see, for example, Stott [4]. Kahneman and Tversky [2] first propose the following value function: Al-Nowaihi et al. [5] show that under preference for homogeneity and loss aversion, the value function will have a power form with identical powers for gains and losses. Tversky and Kahneman [6] estimate the parameters and identify and as median values whereas Abdellaoui [7] estimates a power value function varying in the range . The parameter in (1.2) describes the degree of loss aversion and and measure the degree of diminishing sensitivity. Nonetheless, Levy and Wiener [8], M. Levy and H. Levy [9, 10], Wong, and Chan [11] and others suggest extending the value function in (1.2) without restricting to be greater than one. In this paper, we first study the