0376758 20240103200847.220120608235959.9 Empirical Estimates in Economic and Financial Optimization Problems 20 s. cav_un_epca*02930251212-074XBulletin of the Czech Econometric Society1929 (2012)50-69 stochastic programming empirical estimates moment generating functions stability Wasserstein metric L1-norm Lipschitz property consistence convergence rate normal distribution Pareto distribution Weibull distribution distribution tails simulation cav_un_auth*0108104 Houda Michal Ekonometrie Department of Econometrics E E UTIA-B Department of Econometrics Ústav teorie informace a automatizace AV ČR, v. v. i. 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/2012/E/houda-empirical estimates in economic and financial optimization problems.pdf GAP402/10/1610 GA ČR cav_un_auth*0263483 GAP402/11/0150 GA ČR cav_un_auth*0273629 GAP402/10/0956 GA ČR cav_un_auth*0263482 CEZ:AV0Z10750506 Many applications from economic and nancial practice lead to optimization problems depending on a probability measure. A complete knowledge of the underlying measure is a necessary assumption to determine an exact optimal solution and an exact optimal value. Since this condition is not usually fullled, the solution is often determined using empirical data. Estimates of the optimal value and the optimal solution sets can be obtained by this approach only. Many eorts has been paid to the investigation of the above mentioned estimates. Especially the consistency and the convergence rate have been investigated. However, it was mostly done for classical problems and underlying distributions with thin tails. The aim of this paper is to analyze these estimates from the point of the distribution tails. To this end, first, we recall some known results. We recall stability results based on the Wasserstein metric corresponding to L1 norm and employ them to the case of heavy tails. 2013 BB 2 http://hdl.handle.net/11104/0209079 2012 cav_un_epca*0293025 Bulletin of the Czech Econometric Society 1212-074X Roč. 19 č. 29 2012 50 69