Mathematics in Financial Risk Management

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Mathematics in Financial Risk Management

by Ernst Eberlein of the Universität Freiburg,
Rüdiger Frey of the Universität Leipzig,
Michael Kalkbrener of Deutsche Bank AG, and
Ludger Overbeck of Universität Giessen

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.

AMS Classification: 62P05, 60G51.

Keywords: Quantitative risk management, financial mathematics, credit risk, risk measures, Libor-rate models, Lévy processes.

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