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 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze)

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. This volume includes the five lecture courses givenat the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. Itdeals withinnovative 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:Stochastic Control with Application in Insurance.- Shige Peng: Nonlinear Expectations, Nonlinear Evaluations and Risk Measures.- Walter Schachermayer: Utility maximisation in Incomplete Markets 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 These notes could equally well be entitled "Applications of Filtering in Financial Theory."