Stochastic analysis with statistical and financial applications

Abstract: 

This talk will start with a review of the framework of stochastic analysis, based on mutually adjoint gradient and divergence operators on a probability space, in relation with the stochastic integral representation of random variables. I will then consider several applications including hedging and sensitivity analysis in finance, convex ordering and bounds on option prices, superefficient drift estimation, moments and invariance for Poisson stochastic integrals, and probability approximations.