Before revision: This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of  non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model which is known as a semi-Markov modulated GBM model  .
After revision: This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model which is known as a semi-Markov modulated GBM model .