Markov-modulated affine processes

We study Markov-modulated affine processes (abbreviated MMAPs), a class of Markov processes that are created from affine processes by allowing some of their coefficients to be a function of an exogenous Markov process X. MMAPs largely preserve the tractability of standard affine processes, as their characteristic function has a computationally convenient functional form. Our setup is a substantial generalization of earlier work, since we consider the case where the generator of X is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

In this study, we investigate Markov-modulated affine processes (MMAPs), which are Markov processes created from affine processes by allowing some coefficients to depend on an exogenous Markov process X. MMAPs maintain the tractability of standard affine processes, as their characteristic function has a computationally convenient form. We extend previous work by considering the case where the generator of X is an unbounded operator. We establish the existence of MMAPs using a martingale problem approach, derive the formula for their characteristic function, and examine various mathematical properties.