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 This volume includes the five lecture courses given&nbsp;at the CIME EMS School on Stochastic Methods in Finance held in Bressanone Brixen Italy 2003. It&nbsp;deals with&nbsp;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. TOC: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:&nbsp;Stochastic Control with Application in Insurance. Shige Peng: Nonlinear Expectations Nonlinear Evaluations and Risk Measures. Walter Schachermayer: Utility maximisation in Incomplete Markets