A Note on Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure

0536237 - ÚTIA 2021 RIV CZ eng K - Conference Paper (Czech conference)
Kaňková, Vlasta
A Note on Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure.
Proceedings of the 38th International Conference on Mathematical Methods in Economics. Brno: Faculty of Business Economics, Mendel University, 2020 - (Kapounek, S.; Vránová, H.), s. 247-252. ISBN 978-80-7509-734-7.
[INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS IN ECONOMICS (MME 2020) /38./. Brno (CZ), 09.09.2020-11.09.2020]
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Keywords : Stochastic optimization problem * Nonlinear dependence * Empirical estimates * Static problems
OECD category: Applied Economics, Econometrics
http://library.utia.cas.cz/separaty/2020/E/kankova-0536237.pdf

Nonlinear dependence on a probability measure begins to appear (last time) in a stochastic optimization rather often. Namely, the corresponding type of problems corresponds to many situations in applications. The nonlinear dependence can appear as in the objective functions so in a constraints set. We plan to consider the case of static (one-objective) problems in which nonlinear dependence appears in the objective function with a few types of constraints sets. In details we consider constraints sets “deterministic”, depending nonlinearly on the probability measure, constraints set determined by second order stochastic dominance and the sets given by mean-risk problems. The last case means that the constraints set corresponds to solutions those guarantee an acceptable value in both criteria. To introduce corresponding assertions we employ the stability results based on the Wasserstein metric and L1 norm. Moreover, we try to deal also with the case when all results have to be obtained (estimated) on the data base.
Permanent Link: http://hdl.handle.net/11104/0314174