0468834 20240103213339.020170111235959.9 Praha ÚTIA AV ČR v. v. i. 2016 19 s. P Research Report 2358 Conditional Value-at-Risk Value-at-Risk risk measure cav_un_auth*0280972 Branda Martin Ekonometrie Department of Econometrics E E UTIA-B Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0220207 Červinka Michal Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0332700 Schwartz A. DE http://library.utia.cas.cz/separaty/2016/E/branda-0468834.pdf cav_un_auth*0294967 GA13-01930S GA ČR CZ cav_un_auth*0321507 GA15-00735S GA ČR We deal with investment problems where we minimize a risk measure under a condition on the sparsity of the portfolio. Various risk measures are considered including Value-at-Risk and Conditional Value-at-Risk under normal distribution of returns and their robust counterparts are derived under moment conditions, all leading to nonconvex objective functions. We propose four solution approaches: a mixed-integer formulation, a relaxation of an alternative mixed-integer reformulation and two NLP regularizations. In a numerical study, we compare their computational performance on a large number of simulated instances taken from the literature. We deal with investment problems where we minimize a risk measure under a condition on the sparsity of the portfolio. Various risk measures are considered including Value-at-Risk and Conditional Value-at-Risk under normal distribution of returns and their robust counterparts are derived under moment conditions, all leading to nonconvex objective functions. We propose four solution approaches: a mixed-integer formulation, a relaxation of an alternative mixed-integer reformulation and two NLP regularizations. In a numerical study, we compare their computational performance on a large number of simulated instances taken from the literature. BB 2017 3 4 O 4o 20231122142157.0 RVO:67985556 http://hdl.handle.net/11104/0266849 cav_un_auth*0340903 Matematicko-fyzikalni fakulta UK MFF UK cav_un_auth*0340904 Fakulta socialnich ved UK FSV UK cav_un_auth*0340905 Technische Universitaet Darmstadt DE S 2016 Soubory v repozitáři: 0468834.pdf 2016 Praha ÚTIA AV ČR v. v. i.