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  . We study the well-posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing uniqueness.
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 . In a semi-Markov modulated GBM model the locally risk minimizing price function satisfies a special case of this problem . We study the well-posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing uniqueness.
A
degenerate
R
which is known as
. In
A
the locally risk minimizing price function satisfies a special case of this problem