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Abstract:
Recent developments of stochastic analysis have pushed the theory to previously unknown horizons. Dealing with previously mysterious objects such as white noises, Wick products, non-adapted integrands or anticipating stochastic differential equations has become relatively common in the new developments that have taken place along recent years. Backward stochastic differential equations, forward-backward stochastic differential equations or stochastic partial differential equations with distribution-valued solutions are now part of the classical methodology within this field. The aim of this session is to highlight some of these recent and powerful advances of the theory and to put them in contact with potential applications. In particular, we will focus on their applications to finance, where the information flows can be very important to understand the evolution of wealth processes, and pose difficult technical questions too. Also to physics, since some recent developments, such as stochastic thermodynamics, need of stochastic descriptions that should allow for time reversibility.
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