High frequency data aggregation and Value-at-Risk ; Aukšto dažnio duomenų agregavimas ir vertės pokyčio rizika

VILNIUS UNIVERSITYMilda PranckevičiūtėHigh frequency data aggregation and Value-at-RiskDoctoral dissertationPhysical sciences, Mathematics (01P)Vilnius, 2011The scientific work was carried out during 2006-2010 at Vilnius UniversityScientific supervisor:Prof. Dr. Habil. Alfredas Račkauskas (Vilnius University, Physical Sciences,Mathematics – 01P)VILNIAUS UNIVERSITETASMilda PranckevičiūtėAUKŠTO DAŽNIO DUOMENŲ AGREGAVIMAS IRVERTĖS POKYČIO RIZIKADaktaro disertacijaFiziniai mokslai, matematika (01P)Vilnius, 2011Disertacija rengta 2006-2010 metais Vilniaus universiteteMokslinis vadovas:Prof. habil. dr. Alfredas Račkauskas (Vilniaus universitetas, fiziniai mokslai,matematika – 01P)ContentsIntroduction iii1 Aggregated Value-at-Risk model 11.1 Standard V . . . ..................... 21.1.1 Loss distribution ....................... 31.1.2 Value-at-Risk ......................... 51.2 Aggregated V ...................... 61.3 Numerical example .......................... 81.4 Conclusions .............................. 142 Functionalρ− GARCH(1, 1) model 152.1 Point-wise GARCH 172.2 Model................................. 202.3 Stationarity 202.4 Estimation............................... 242.5 Some examples ............................ 292.6 Conclusions .............................. 333 uvGARCH(1, 1) model in a Hilbert space 343.1 Model 353.2 Stationarity 363.3 Estimation 393.3.1 Consistency .......................... 413.3.2 Asymptotic normality ......