"Project is focused on analysis of fin. market processes, and prediction of firm default by real options approach. Pricing of fin. derivatives, Am. options in particular, forms our main issue, since it leads to nonlinear BVP defined within a framework of variational inequalities theory. We implement FEM for num. solving of such problems. The FE with polynomial basis may have curved boundaries and surfaces suitable for solving pricing problems of compound options with time-dependent free boundaries of optimal exercising. This procedure is used for analysis and pricing of real options, which are to characterize firm market value. Estimation and prediction of firm default in framework of real options is approached using barrier stoch. process representing a firm market trajectory. Time of firm default is defined by barrier hitting-time. We concern also development of tech. analysis of stocks based upon Markov chains, and connections of firm default estim. methods proposed with classical ones. Project issues will be publications in impact journals and presentations on int. conferences."@en . "2015-01-01+01:00"^^ . "Modelov\u00E1n\u00ED proces\u016F na finan\u010Dn\u00EDch trz\u00EDch a predikce bankrotu firem apar\u00E1tem re\u00E1ln\u00FDch opc\u00ED" . . . . " finite element method" . . "2016-12-31+01:00"^^ . "1"^^ . "0"^^ . " technical analysis of stocks" . "Option pricing" . . "http://www.isvav.cz/projectDetail.do?rowId=GA15-20405S"^^ . "0"^^ . "Projekt je zam\u011B\u0159en na anal\u00FDzu proces\u016F na fin. trz\u00EDch a predikci \u00FApadku firmy apar\u00E1tem re\u00E1ln\u00FDch opc\u00ED. Hlavn\u00EDm t\u00E9matem je oce\u0148ov\u00E1n\u00ED fin. deriv\u00E1t\u016F, p\u0159edev\u0161\u00EDm americk\u00FDch opc\u00ED, kter\u00E9 vedou na neline\u00E1rn\u00ED okrajov\u00E9 \u00FAlohy, kter\u00E9 lze formulovat pomoc\u00ED varia\u010Dn\u00EDch nerovnic. Pro jejich num. \u0159e\u0161en\u00ED u\u017E\u00EDv\u00E1me metodu kone\u010Dn\u00FDch prvk\u016F. Prvky s polynom. aprox. funkcemi maj\u00ED k\u0159iv\u00E9 hrany a st\u011Bny vhodn\u00E9 pro \u0159e\u0161en\u00ED \u00FAloh ocen\u011Bn\u00ED slo\u017Een\u00FDch opc\u00ED s volnou hranic\u00ED optim\u00E1ln\u00ED realizace. Tento apar\u00E1t u\u017E\u00EDv\u00E1me t\u00E9\u017E k anal\u00FDze a ocen\u011Bn\u00ED re\u00E1ln\u00FDch opc\u00ED charakterizuj\u00EDc\u00EDch tr\u017En\u00ED hodnotu firem. Odhad a predikci \u00FApadku firmy formulujeme a num. \u0159e\u0161\u00EDme, v r\u00E1mci apar\u00E1tu re\u00E1ln\u00FDch opc\u00ED, pomoc\u00ED bari\u00E9rov\u00E9ho stoch. procesu, kter\u00FD vystihuje trajektorii firmy v tr\u017En\u00EDm prost\u0159ed\u00ED. Okam\u017Eik \u00FApadku firmy je vyj\u00E1d\u0159en okam\u017Eikem n\u00E1razu na bari\u00E9ru. Pozornost v\u011Bnujeme i rozpracov\u00E1n\u00ED metod tech. anal\u00FDzy akci\u00ED pomoc\u00ED Markovov. \u0159et\u011Bzc\u016F, a d\u00E1le propojen\u00ED navr\u017Een\u00FDch metod predikce \u00FApadku firmy s klasick\u00FDmi bonitn\u00EDmi p\u0159\u00EDstupy. V\u00FDstupem projektu budou p\u0159edev\u0161\u00EDm publikace v impaktovan\u00FDch \u010Dasopisech a prezentace na mezin\u00E1rodn\u00EDch konferenc\u00EDch." . . "0"^^ . "GA15-20405S" . . . " real options" . "Modelling of processes on financial markets and prediction of firm default by real options"@en . "0"^^ . . . "2015-04-23+02:00"^^ . "Option pricing; numerical methods; finite element method; prediction of firm default; real options; technical analysis of stocks; Markov chains"@en . . . . . . . " numerical methods" . . " prediction of firm default" .