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Markov-modulated affine processes

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  • Kurt, Kevin
  • Frey, Rüdiger

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 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.

Suggested Citation

  • Kurt, Kevin & Frey, Rüdiger, 2022. "Markov-modulated affine processes," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 391-422.
    • Handle: RePEc:eee:spapps:v:153:y:2022:i:c:p:391-422
    DOI: 10.1016/j.spa.2022.08.009
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