Martingale driven BSDEs, PDEs and other related deterministic problems
arXiv:1707.07879
Abstract
We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.
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- BSDEs with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples