Mild solutions to path-dependent PDEs

The recent functional extension of the widely applied Itô formula by Dupire, Cont, and Fournié led to the new exciting class of path-dependent partial differential equations (PPDEs). In relevant publications, the most... [ view full abstract ]

The recent functional extension of the widely applied Itô formula by Dupire, Cont, and Fournié led to the new exciting class of path-dependent partial differential equations (PPDEs). In relevant publications, the most common approach to construct classical or viscosity solutions to PPDEs is to utilize backward stochastic differential equations (BSDEs). In this talk, we rely instead on Markovian integral equations and present path-dependent diffusions to give a general existence and uniqueness result for mild solutions to semilinear parabolic PPDEs. Moreover, we motivate this solution concept by applications in option pricing models.