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Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients, which is shown to be a weighted-mean trimmed region. Given an external sample of the coefficients, an uncertainty set is a convex polytope that can be exactly calculated. We construct an efficient geometrical algorithm to solve stochastic linear programs that have a single distortion risk constraint. The algorithm is available as an R-package. Also the algorithms asymptotic behavior is investigated, when the sample is i.i.d. from a general probability distribution. Finally, we present some computational experience.
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the w
Stream constraint programming is a recent addition to the family of constraint programming frameworks, where variable domains are sets of infinite streams over finite alphabets. Previous works showed promising results for its applicability to real-wo
Constraint programming (CP) is a paradigm used to model and solve constraint satisfaction and combinatorial optimization problems. In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree searc
This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically
We are concerned with the linear-quadratic optimal stochastic control problem with random coefficients. Under suitable conditions, we prove that the value field $V(t,x,omega), (t,x,omega)in [0,T]times R^ntimes Omega$, is quadratic in $x$, and has the