Comparative statics and portfolio choices under the phantom decision model

This study characterizes attitudes toward uncertainty in the phantom decision model introduced by Izhakian and Izhakian (2015) and conducts a comparative statics analysis to examine how changes in phantom uncertainty and phantom aversion affect portfolio choices. First, “phantom averse” and “more phantom-averse” are defined in a manner that differs from Izhakian and Izhakian (2015). Assuming that utility functions have realization forms, the above notions are characterized by the shapes of their reduction components. For the portfolio choice problem that consists of one safe asset and one phantom asset, we derive sufficient conditions under which changes in phantom uncertainty and phantom aversion monotonically decrease the investment in the phantom asset. Some familiar concepts in expected utility theory are extended to the framework of the phantom decision model.