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Probability and Computational Finance Seminar
Mihai Sirbu University of Texas at Austin Title: Stochastic Perron's method in linear and non-linear problems 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. Date: Monday, October 8, 2012 Time: 5:00 pm Location: Wean Hall 6423 Submitted by: Dmitry Kramkov |