In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the `true’ covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider … Read more
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value when the stochastic program is expressed in terms of a law invariant coherent risk measure having a discrete Kusuoka representation. The obtained results … Read more
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied … Read more
In this paper we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We also discuss consistency and rates of convergence of sample average approximations of such stochastic problems. CitationSchool of Industrial and … Read more