Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

We discuss the concept and motivation of quasiderivatives and give an example constructed by random time change, Girsanov's theorem and Levy's theorem. Then we use this probabilistic method to investigate the smoothness and estimate the derivatives of the probabilistic solution of the Dirichlet problem for degenerate elliptic equations, from linear cases to fully nonlinear cases. In each Dirichlet problem we consider, the probabilistic solution is the unique solution in our setting. This work is under the guidance of my advisor Nicolai V. Krylov.

Speaker: Wei Zhou, University of Minnesota