论文信息 - Convexification of Stochastic Ordering

Convexification of Stochastic Ordering

We consider sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed convex hull of the first set is equal to the second set.

A. Ruszczynski | D. Dentcheva

[1] H. B. Mann,et al. On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other , 1947 .

[2] E. Lehmann. Ordered Families of Distributions , 1955 .

[3] J. Quirk,et al. Admissibility and Measurable Utility Functions , 1962 .

[4] V. Strassen. The Existence of Probability Measures with Given Marginals , 1965 .

[5] Josef Hadar,et al. Rules for Ordering Uncertain Prospects , 1969 .

[6] Peter C. Fishburn,et al. Utility theory for decision making , 1970 .

[7] I. Olkin,et al. Inequalities: Theory of Majorization and Its Applications , 1980 .

[8] K. Mosler,et al. Stochastic orders and decision under risk , 1991 .

[9] R. Szekli. Stochastic Ordering and Dependence in Applied Probability , 1995 .

[10] Elja Arjas,et al. Bayesian Inference of Survival Probabilities, under Stochastic Ordering Constraints , 1996 .

[11] A. Müller,et al. Comparison Methods for Stochastic Models and Risks , 2002 .

[12] W. N. King,et al. Minimum distance estimation of the distribution functions of stochastically ordered random variables , 2002 .

[13] Dudley,et al. Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[14] Darinka Dentcheva,et al. Optimization under linear stochastic dominance , 2003 .

[15] Darinka Dentcheva,et al. Optimization with Stochastic Dominance Constraints , 2003, SIAM J. Optim..