Increasing Risk: Some Direct Constructions

This article extends the classic RothschildNStiglitz characterization of comparative risk ("increasing risk") in two directions. By adopting a more general definition of "mean preserving spread" (MPS), it provides a direct construction of a sequence of MPS's linking any pair of distributions that are ranked in terms of comparative risk. It also provides a direct, explicit construction of a zero-conditional-mean "noise" variable for any such pair of distributions. Both results are extended to the case of second order stochastic dominance.