Crash hedging strategies and optimal portfolios [Elektronische Ressource] / Olaf Arnd Menkens

¨Technische Universitat KaiserslauternCrash Hedging StrategiesandOptimal Portfoliosc Olaf Arnd MenkensVom Fachbereich Mathematik¨der Technischen Universitat Kaiserslauternzur Verleihung des akademischen GradesDoktor der Naturwissenschaften(Doctor rerum naturalium, Dr. rer. nat.)genehmigte Dissertation1. Gutachter: Prof. Dr. Ralf Korn2. Gutachter: Prof. Dr. Mogens SteffensenDatum der Disputation: 30.11.2004D 386AbstractIn traditional portfolio optimization under the threat of a crash theinvestment horizon or the time to maturity is neglected.Developing the so–called crash hedging strategies (which are portfoliostrategies which make an investor indifferent to the occurrence of an un-certain (down) jumps of the price of the risky asset) the time to maturityturns out to be essential. The crash hedging strategies are derived as solu-tions of non–linear differential equations which itself are consequences of aequilibrium strategy. Hereby the situation of changing market coefficientsafter a possible crash is considered for the case of logarithmic utility aswell as for the case of general utility functions. A benefit–cost analysis ofthe crash hedging strategy is done as well as a comparison of the crashhedging strategy with the optimal portfolio strategies given in traditionalcrash models.Moreover, it will be shown that the crash hedging strategies optimizethe worst–case bound for the expected utility from final wealth subject tosomerestrictions.