We analyze pricing and portfolio optimization problems in defaultable regime switching markets driven by a underlying continuous-time Markov process. We contribute to both of these problems by obtaining new representations of option prices and optimal portfolio strategies under regime-switching. Using our option price representation, we develop a novel efficient method to price claims which may...

The fast marching method (FMM) has proved to be a very efficient algorithm for solving the isotropic Eikonal equation. Because it is a minor modification of Dijkstra’s algorithm for finding the shortest path through a discrete graph, FMM is also easy to implement. In this paper we describe a new class of Hamilton–Jacobi (HJ) PDEs with axis-aligned anisotropy which satisfy a causality condition ...