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...

We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete markets model. An assumption of "smallness'' type - imposed through the new notion of "closeness to Pareto optimality'' - is shown to be sufficient for existence and uniqueness. Central role in our...

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model...