PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Anna Mazzucato, Victor Nistor, Stephanie Zerby.

Title:Stochastic Perron's method in linear and non-linear problems
Seminar:Probability and Financial Mathematics Seminar
Speaker:Mihai Sirbu, University of Texas, Austin, Mathematics
Abstract:
We introduce a stochastic version of the classical Perron's method to construct viscosity solutions to linear parabolic equations associated to stochastic differential equations. Using this method, we construct easily two viscosity (sub and super) solutions that squeeze in between the expected payoff. If a comparison result holds true, then there exists a unique viscosity solution which is a martingale along the solutions of the stochastic differential equation. The unique viscosity solution is actually equal to the expected payoff. This amounts to a verification result (Ito's Lemma) for non-smooth viscosity solutions of the linear parabolic equation. We show how the method can be extended to non-linear problems, like free boundary problems associated to optimal stopping or Dynkin games and Hamilton-Jacobi-Bellman equations in stochastic control. The presentation is based on joint work with Erhan Bayraktar.

Room Reservation Information

Room Number:MB114
Date:01 / 29 / 2013
Time:03:45pm - 05:00pm