0359099 20240103195125.920110601235959.9 11 s. cav_un_epca*0359063978-80-7043-773-59-19PlzeňZápadočeská univerzita v Plzni2010LukášLadislav stochastic programming problems L_1 norm Lipschitz property empirical estimates convergence rate exponential tails heavy tails Pareto distribution risk functional cav_un_auth*0101122 Kaňková Vlasta Ekonometrie Department of Econometrics E E UTIA-B Department of Econometrics Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2011/E/kankova-empirical estimates in stochastic optimization special cases.pdf GAP402/10/0956 GA ČR cav_un_auth*0263482 GA402/07/1113 GA ČR cav_un_auth*0228801 GA402/08/0107 GA ČR CZ cav_un_auth*0240545 GA402/06/0990 GA ČR CZ cav_un_auth*0215013 CEZ:AV0Z10750506 Classical optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are relatively complicated. On the other hand, these problems fulfil very often "suitable" mathematical properties guaranteing the stability (w.r.t. probability measure) and, moreover, giving a possibility to replace the "underlying" probability measure by an empirical one to obtain "good" stochastic estimates of the optimal value and the optimal solution. Properties of thess estimates have been investigated mostly for standard types of probability measures with suitable (thin) tails and independent random samples. However distributions with heavy tails correspond to many economic problems and, moreover, many applications do not correspond to the "classical" problems. The aim of the paper is, first, to try to recall stability results including also heavy tails and more general problems. cav_un_auth*0271670 Výpočtová ekonomie, 4. seminář Plzeň 18.12.2008 CZ 2012 BB http://hdl.handle.net/11104/0196952 2010 cav_un_epca*0359063 Výpočtová ekonomie, sborník 4.semináře 978-80-7043-773-5 9 19 Computational Economy, Proceedings of the Fourth Seminar Plzeň Západočeská univerzita v Plzni 2010 Lukáš Ladislav 340