Stochastic Methods in Finance [electronic resource] : Lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6-12, 2003 / by Kerry Back, Tomasz R. Bielecki, Christian Hipp, Shige Peng, Walter Schachermayer.

Preface -- Kerry Back: Incomplete and Asymmetric Information in Asset Pricing Theory -- Tomasz R. Bielecki, Monique Jeanblanc, Marek Rutkowski: Modeling and Valuation of Credit Risk -- Christian Hipp: Stochastic Control with Application in Insurance -- Shige Peng: Nonlinear Expectations, Nonlinear Evaluations and Risk Measures -- Walter Schachermayer: Utility Maximisation in Incomplete Markets.

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.