Stochastic Dominance Constraints
Stochastic dominance relations may be used as constraints in problems of mathematical optimization, in particular stochastic programming. In a problem of maximizing a real functional over random variables in a set we may additionally require that stochastically dominates a fixed random benchmark . In these problems, utility functions play the role of Lagrange multipliers associated with stochastic dominance constraints. Under appropriate conditions, the solution of the problem is also a (possibly local) solution of the problem to maximize over in, where is a certain utility function. If the first order stochastic dominance constraint is employed, the utility function is nondecreasing; if the second order stochastic dominance constraint is used, is nondecreasing and concave.
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