Some new aspects of optimal portfolios and option pricing [Elektronische Ressource] / Martin Krekel

Universitat KaiserslauternFachbereich MathematikSome new aspects ofOptimal Portfolios and Option PricingMartin KrekelVom Fachbereich Mathematikder Universit at Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Ralf Korn2. Gutachter: Prof. Dr. Mogen Ste ensenDatum der Disputation: 20.06.2003D 386.IntroductionThe main two problems of continuous-time nancial mathematics are option pricingand portfolio optimization. The rst of these problems is concerned with valuing derivativecontracts on stocks (or other underlyings) which have a non-linear payo structure such asall kind of options. The other important topic, portfolio optimization, consists of the searchfor the best investment strategy of an investor who is trading securities at a nancial market.In this thesis, various new aspects of the above major topics of nancial mathemat-ics will be discussed. In all our considerations we will assume the standard di usion typesetting for securitiy prices which is today well-know under the term "Black-Scholes model".This setting and the basic results of option pricing and portfolio optimization are surveyedin the rst chapter.The next three chapters deal with generalizations of the standard portfolio problem,also know as "Merton’s problem".