Mild and viscosity solutions to semilinear parabolic path-dependent PDEs
File(s)1611.08318v3.pdf (315.7 KB)
Working paper
Author(s)
Kalinin, A
Schied, A
Type
Working Paper
Abstract
We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The aim of this paper is to show that mild solutions are also solutions in a viscosity sense. This result is motivated by the fact that mild solutions can provide value functions and optimal strategies for problems of stochastic optimal control. Since unique mild solutions exist under weak conditions, we obtain as a corollary a general existence result for viscosity solutions to semiilinear parabolic PPDEs.
Date Issued
2018-11-14
Identifier
http://arxiv.org/abs/1611.08318v3
Subjects
math.PR
math.PR
math.AP
math.OC
60H10, 60H30, 60J68, 35D40, 35D30, 35K10, 93E20
math.PR
math.PR
math.AP
math.OC
60H10, 60H30, 60J68, 35D40, 35D30, 35K10, 93E20