Stochastic Methods in Finance

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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.