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

After some preliminaries, I will present a new type of local asymptotic formula for the Green's function G_t(x,y) of a uniformly parabolic linear operator with non-constant coefficients, obtained using dilations and Taylor expansions at a point z(x,y), for a function z with bounded derivatives such that z(x,x)=x. Our method is based on a Dyson series expansion of the resulting Taylor approximation. The resulting time ordered products can be computed using the Baker-Campbell-Hausdorff commutator formula. Our procedure leads to an elementary, algorithmic construction of approximate solutions to parabolic equations which are accurate to arbitrary prescribed order in the short-time limit. We establish mapping properties and precise error estimates in exponentially weighted, L^p-type Sobolev spaces that appear in practice. Numerical test show the usefulness of such approximations. This is part of joint works with R. Constantinescu, N. Costanzino, J. Liechty, A. Mazzucato, and W. Cheng.

Speaker: Victor Nistor, Penn State UniversitySpeaker: Victor Nistor, Penn State UniversitySpeaker: Victor Nistor, Penn State University

Slides: (TBA)