Stochastic methods in finance

The volume collects the five lecture courses given at the CIME-EMS School on “Stochastic Methods in Finance” held in Bressanone, Italy 2003. It deals of innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modeling 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 non linear 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.