Increasing risk: Some direct constructions. (English) Zbl 0886.90052

Machina, Mark J.; Pratt, John W.

J. Risk Uncertain. 14, No. 2, 103-127 (1997).

Summary: This article extends the classic Rothschild-Stiglitz 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.

MSC:

91B30

Risk theory, insurance (MSC2010)

Keywords:

risk; comparative risk; increasing risk; mean preserving spread; noise; stochastic dominance