Markov-modulated affine processes

Publication: Scientific journalJournal articlepeer-review

Abstract

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 . 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  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.
Original languageEnglish
Pages (from-to)391-422
JournalStochastic Processes and their Applications
Volume153
DOIs
Publication statusPublished - Nov 2022

Austrian Classification of Fields of Science and Technology (ÖFOS)

  • 101007 Financial mathematics
  • 101019 Stochastics

Keywords

  • Markov processes
  • Affine processes
  • Martingale problem
  • Analytical tractability
  • Pricing of financial instruments
  • Markov processes with discontinuous coefficients

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