Mathematics in Financial Risk Management

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 Subject Classification:62P05, 60G51