Displaying similar documents to “Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance”

Thin and heavy tails in stochastic programming

Vlasta Kaňková, Michal Houda (2015)

Kybernetika

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Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the...

Empirical estimates in stochastic optimization via distribution tails

Vlasta Kaňková (2010)

Kybernetika

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“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied...

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

Vlasta Kaňková, Vadim Omelčenko (2018)

Kybernetika

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Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem 𝒰 of the utility functions. Especially, considering 𝒰 : = 𝒰 1 (where 𝒰 1 is a system of non decreasing concave nonnegative utility functions)...

Multistage stochastic programs via autoregressive sequences and individual probability constraints

Vlasta Kaňková (2008)

Kybernetika

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The paper deals with a special case of multistage stochastic programming problems. In particular, the paper deals with multistage stochastic programs in which a random element follows an autoregressive sequence and constraint sets correspond to the individual probability constraints. The aim is to investigate a stability (considered with respect to a probability measures space) and empirical estimates. To achieve new results the Wasserstein metric determined by ℒ 1 norm and results of...

Uniform Lipschitz estimates in stochastic homogenization

Scott Armstrong (2014)

Journées Équations aux dérivées partielles

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We review some recent results in quantitative stochastic homogenization for divergence-form, quasilinear elliptic equations. In particular, we are interested in obtaining L ∞ -type bounds on the gradient of solutions and thus giving a demonstration of the principle that solutions of equations with random coefficients have much better regularity (with overwhelming probability) than a general equation with non-constant coefficients.