Credit risk modeling with random fields [Elektronische Ressource] / vorgelegt von Thorsten Schmidt

Credit Risk Modelingwith Random FieldsInaugural-Dissertationzur Erlangung des Doktorgradesan den Naturwissenschaftlichen Fachbereichen(Mathematik)der Justus-Liebig-Universit at Gie envorgelegt vonThorsten SchmidtGie en 2003D - 26Dekan: Prof. Dr. Albrecht BeutelspacherGutachter: Prof. Dr. Winfried Stute (Gie en)Prof. Dr. Ludger OverbeckDatum der Disputation: 11.09.2003PrefaceThe demand for investments with higher returns in areas other than the stock market hasincreased enormously due to the stock market crash in the last two years. In exchangefor an attractive yield the investors take a credit risk, and as a result methodologies forpricing and hedging credit derivatives as well as for risk management of credit risky assetsbecame very important. The e orts of the Basel Committee is just one of many exampleswhich substantiate this.In the last years the credit markets developed at a tremendous speed while at the sametime the number of corporate defaults increased dramatically. It is therefore not surprisingthat the demand for credit derivatives is growing rapidly.In view of this, the goal of this work is twofold. In the rst part, a survey of the creditrisk literature is given, which o ers a quick introduction into the area and presents themathematical methods in a unifying way. Second, we propose two new models of creditrisk, focusing on di eren t needs. The rst model generalizes existing models using random elds in Hilbert spaces.