Path-dependent PDEs and anon-Markovian vanishing viscosity result
The non-exponential Schilder-type theorem in Backhoff-Veraguas, Lacker and Tangpi [Ann. Appl. Probab. (2020), pp. 1321-1367] is expressed as a convergence result for path-dependent PDEs with appropriate notions of generalized solutions. This entails a non-Markovian counterpart to the vanishing viscosity method.
To this end, we show uniqueness of maximal subsolutions for path-dependent viscous Hamilton-Jacobi equations associated to convex superquadratic backward stochastic differential equations. Thereby, we obtain a corresponding non-Markovian Feynman-Kac formula.
We also study the Bellman equation associated to a Bolza problem of the calculus of variations with path-dependent terminal cost. In particular, uniqueness among lower semicontinuous solutions holds and state constraints can be admitted.
This talk is based on joint work with Erhan Bayraktar.
Bio: Christian Keller is an assistant professor in the Department of Mathematics at the University of Central Florida.
Previously, he was a Donald J. Lewis Research Assistant Professor of Mathematics at the University of Michigan.
He obtained his Ph.D. in Applied Mathematics at the University of Southern California. His research interests are
path-dependent partial differential equations and applications in stochastic optimal control and mathematical finance.