A wavelet tour of option pricing [Elektronische Ressource] / vorgelegt von Roman Mario Xerxes Rometsch

Universitat UlmFakultat fur Mathematik undWirtschaftswissenschaftenA Wavelet Tour of Option PricingDissertationzur Erlangung des Doktorgrades Dr. rer. nat.der Fakultat fur Mathematik und Wirtschaftswissenschaften der Universitat Ulmvorgelegt vonRoman Mario Xerxes Rometschaus Ulm2010Amtierender Dekan: Prof. Dr. Werner Kratz1. Gutachter: Prof. Dr. Karsten Urban2. Gutachter: Prof. Dr. Rudiger KieselTag der Promotion: 29. Oktober 2010A Wavelet Tour of Option PricingAdaptive Wavelet Methodsfor Variational Inequalities2010 Mathematics Subject Classi cation: 35J20, 35J61, 35J86, 35K85,35Q68, 41A25, 45E05, 49J40,65K15, 65R20, 65T60, 91G80c2010 Mario RometschPlease report errors to: mario.rometsch@googlemail.comto SabrinaAbstractThe e cient numerical solution of elliptic variational inequalities in generaland of obstacle problems in particular is of great interest and poses a nontrivialchallenge in Numerical Mathematics. Such problems occur for example afterthe time-discretization of the pricing problem of an American option.The algorithm EVISOLVE, that is presented in this thesis, consists of anadaptive wavelet method that allows for an e cient and reliable solution of suchelliptic inequalities. Adaptivity means that the algorithm uses results to adjustitself in order to keep the convergence rate optimal also for nonsmooth solutionsand to estimate the error such that a prespeci ed accuracy can be guaranteed.