Stochastic methods in finance: lectures given at the C.I.M.E.-E.M.S. summer school held in Bressanone/Brixen, Italy, July 6-12, 2003

Kerry Back, Tomasz R. Bielecki, Christian Hipp, Shige Peng, Walter Schachermayer (auth.)9783540229537, 3540229531

This volume includes the five lecture courses given at the CIME-EMS School on “Stochastic Methods in Finance” held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topics are treated in detail: Utility maximization in incomplete markets; the theory of nonlinear expectations and its relationship with the theory of risk measures in a dynamic setting; credit risk modelling; the interplay between finance and insurance; incomplete information in the context of economic equilibrium and insider trading.

Table of contents :
Incomplete and Asymmetric Information in Asset Pricing Theory….Pages 1-25
Modeling and Valuation of Credit Risk….Pages 27-126
Stochastic Control with Application in Insurance….Pages 127-164
Nonlinear Expectations, Nonlinear Evaluations and Risk Measures….Pages 165-253
Utility Maximisation in Incomplete Markets….Pages 255-293