A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasiconvex, nor...

Probabilistic risk beliefs are key drivers of economic and health decisions, but people are not always certain about their beliefs. We study these "imprecise probabilities", also known as ambiguous beliefs. We show that imprecision is measurable separately from the levels of risk beliefs. People...