20.500.12556/RUL-159095 Problem optimalnega ustavljanja Brownovega mostu magistrsko delo The problem of optimal stopping of a Brownian bridge V delu obravnavamo optimalen čas ustavljanja Brownovega mostu in funkcionala Brownovega mostu. Spomnimo se nekaterih osnovnih pojmov, kot so filtracije, martingali in Brownovo gibanje. S pomočjo slučajnih procesov poskušamo poiskati lastnosti Brownovega mostu ter si s tem pomagati pri izračunu optimalnega časa ustavljanja, pri čemer uporabimo tudi znanje reševanja diferencialnih enačb. Pogledamo si še optimalen čas ustavljanja lihe potence, preslikanega in integrala Brownovega mostu. Omenjene krivulje nato simuliramo v programu R. This work studies optimal stopping time of a Brownian bridge and functional of a Brownian bridge. We recall some basic terms as filtrations, martingales and Brownian motion. We study their properties using stochastic processes. We solve optimal stopping problem, and several related problems, using knowledge of solving differential equations. We also study some related problems where the gain functions are certain functionals of a Brownian bridge. Odd powers, reflected and integral of a Brownian bridge is considered. For simulation we use program R. Brownov most Brownovo gibanje Itova formula martingal lokalni martingal navadna diferencialna enačba optimalen čas ustavljanja Brownian bridge Brownian motion Ito's lemma martingal local martingal ordinary differential equation optimal stopping time true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-06-29 08:15:16 2024-06-29 08:15:17 2024-07-11 03:46:18 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 139862 200147971 12110.pdf 12110.pdf 1 D4691EC19E8B4332098CCC9327907D2C f408a17f77eacd7936977b0c823eb8e45c59a15f639905ae7c7767ce83049a43 f4ec71fc-35de-11ef-860e-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186964 12111.R 12111.R 1 20BF7BE2FB616EFF2710ED07B622407E ccafbecc68f134ce278f65d424b9d0595db410d7a5bdf6eb3435110fd60f35ed f4ecbe2d-35de-11ef-860e-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186965 12112.R 12112.R 1 2B9FF9813BBAE290C5E6AB288DAE863C 61d5504686a1242758049b7d437357ae90be8caa9b9c0977e30a44139de6180c f4eef80f-35de-11ef-860e-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186966 12113.R 12113.R 1 6286F25E7FEB748849C40925CE40EF68 8d776c3d3f75dd9ff05cc443b187f1267d700fd6d240f52e26de16d61a489b6c f4ef238c-35de-11ef-860e-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186967 12114.R 12114.R 1 9F8F63D825BE5ADA6530CDA8185C53A5 37e96ba9e679efc5fca774898f1eaac8f6a3d56bbccc6d9d282c022e826ec0b4 f4ef50c6-35de-11ef-860e-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=186968 Fakulteta za matematiko in fiziko 0 0 0