Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance

Abstract

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Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

“…Lemma 3.2. (Kaňková [4]) Let g(x, z), Y (z) be for every x ∈ X Lipschitz functions of z ∈ IR s with the Lipschitz constant L g not depending on x ∈ X. Let, moreover,…”

“…Lemma 3.3. (Kaňková [4]) Let X be a nonempty compact set, P F , P G ∈ M 1 1 (IR s ), Assumption A.1 be fulfilled. Let, moreover, g(x, z), Y (z) be for every x ∈ X Lipschitz functions of z ∈ Z F ∪ Z G with the Lipschitz constant L g not depending on x ∈ X.…”

“…Proposition 3.4. (Kaňková [4]) Let X be a nonempty compact set, P F , P G ∈ M 1 1 (IR s ), Assumptions A.0, A.1 be fulfilled. Let, moreover, g(x, z), Y (z) be for every…”

Slot Allocation in a Multi-airport System under Flying Time Uncertainty

“…20) A second group of methods transforms chance constraints into deterministic constraints based on the method of stochastic programming or distribu-tionally robust optimization. 21,22) To capture the constraints from shared resources in slot allocation for a MAS, the authors first propose a certainty slot allocation model (CSAM). Next, the fix capacity constraints are modeled as chance constraints to consider the uncertainty of flying times.…”

Estimaciones de estabilidad en modelos colectivos de riesgo

“…Por ejemplo, en Beirlant and Rachev (1987) y Rachev (1991) hay resultados de este tipo para el modelo Sparre Andersen. En Gordienko (2004) se demuestra una desigualdad de estabilidad para la distribución de R(t) en modelos generales pero bajo la restricción de que D(N (t)) = D( N (t)). Sobre la estabilidad de D(R(t)) para procesos multidimensionales de riesgo, no se encontraron resultados en la literatura relacionados con este tipo de desigualdades.…”