0502907 20240903170642.220190314235959.9 85064204073 000457070200010 10.14736/kyb-2018-6-1231 16 s. P cav_un_epca*02971630023-5954546 (2018)1231-1246Ústav teorie informace a automatizace AV ČR, v. v. i. Stochastic programming problems Second order stochastic dominance constraints Wasserstein metric Stability Relaxation Scenario generation Empirical estimates Light-and heavy tailed distributions Crossing cav_un_auth*0101122 Department of Econometrics 75 Kaňková Vlasta UTIA-B Ekonometrie Department of Econometrics E E K Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0271480 Omelchenko Vadym UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics CZ Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2019/E/kankova-0502907.pdf cav_un_auth*0363963 GA18-02739S GA ČR 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_ is a system of a non decreasing concave nonnegative utility functions) we obtain second order stochastic dominance constraints. Unfortunately it is also known that these problems are rather complicated as from the theoretical and the numerical point of view. Moreover, these problems go to semi-infinite optimization problems for which Slater's condition is not necessary fulfilled. Consequently it is suitable to modify the constraints. A question arises how to do it. The aim of the paper is to suggest one of the possibilities how to modify the original problem with an „estimation“ of a gap between the original and modified problem. To this end the stability results obtained on the base of the Wasserstein metric corresponding to L_1 norm are employed. Moreover, we mention a scenario generation and an investigation of empirical estimates. At the end attention will be paid to heavy tailed distributions. cav_un_auth*0373587 19th Joint Czech -German-Slovak Conference on Mathematical Methods in Economy and Industry (MMEI) 20180604 20180606 Jindřichův Hradec CZ WOS BB 10000 10100 10103 2019 2 RVO:67985556 http://hdl.handle.net/11104/0295272 S 3+4 Article|Proceedings Paper Computer Science Cybernetics COMPUTERSCIENCE.CYBERNETICS 0.591 0.155 13 0.00068 0.174 891 0.268 0.500 71 Q4 15.991 6.5 Q4 Q3 0.17 Q4 6.522 2018 85064204073 SCOPUS PUBMED 000457070200010 WOS cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 54 č. 6 2018 1231 1246 Ústav teorie informace a automatizace AV ČR, v. v. i.