Mathematics in Financial Risk Management
by Ernst Eberlein of the Universität Freiburg,
March 31, 2007
Abstract: The paper gives an overview of mathematical models and methods used in financial risk management; the main area of application is credit risk. A brief introduction explains the mathematical issues arising in the risk management of a portfolio of loans. The paper continues with a formal overview of credit risk management models and discusses axiomatic approaches to risk measurement. We close with a section on dynamic credit risk models used in the pricing of credit derivatives. Mathematical techniques used stem from probability theory, statistics, convex analysis and stochastic process theory.
Keywords: Quantitative risk management, financial mathematics, credit risk, risk measures, Libor-rate models, Lévy processes.