Abstract : We obtain the existence and uniqueness of a classical solution to a Cauchy problem for a quasilinear parabolic partial integro-differential equation (PIDE) which arises due to its association with a forward-backward stochastic differential equation (FBSDEs) with jumps. More specifically, we embed the associated PIDE into a suitable class of non-local quasilinear parabolic PDEs which allows us to extend the methodology of Ladyzhenskaya et al (O. Ladyzenskaja, V. Solonnikov, N.N. Uralceva. Linear and Quasi-Linear Equations of Parabolic Type, 1968) to non-local PDEs of this class. The maximum principle, gradient estimate, and Hölder norm estimates are obtained in order to show the existence of a solution to an initial-boundary value problem by means of the Leray-Schauder theorem. The existence of a classical solution to the Cauchy problem is then obtained by employing the diagonalization argument.

Venue: DIM seminar room, Beauchef 851, 4th floor.

Zoom: https://uchile.zoom.us/j/96642349167?pwd=MkRVbWxzOFBUUXlCTWFicW0reWZ6dz09