Pathwise integration, Malliavin calculus and stochastic control

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This project is concerned with the development of pathwise integration techniques in the scope of Malliavin calculus. The main applications will be new classifications for stochastic processes, development of new numerical methods and new theoretical developments in stochastic optimal control taking advantage of the new pathwise interpretation paradigm. The project takes inspiration in the marriage between analysis and probability by creating and developing tools specific to one field and applying them to the other. The project leads lastly to applications in path-dependent partial differential equations. These appear naturally within the scope of stochastic optimal control problems involving so-called path-dependent contracts when using the pathwise technique. Addressed is also the deeper issue of giving meaning to martingales from a pathwise point of view.