Jump-Diffusion Processes with Regime Switching

Nikita Ratanov and Alexander D. Kolesnik
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Nikita Ratanov: Chelyabinsk State University
Alexander D. Kolesnik: Institute of Mathematics and Computer Science

Chapter 4 in Telegraph Processes and Option Pricing, 2022, pp 189-221 from Springer

Abstract: Abstract In this chapter, we examine a modification of the standard steady state process obtained by adding a diffusion component. We give a detailed description of Markov-modulated jump-diffusion processes and their properties, as well as the jump-diffusion martingales and the Girsanov measure transformation, and we introduce the concept of relative entropy. This model has infinitely many equivalent martingale measures. Surprisingly, it turns out that the Esscher transform does not give the minimum relative entropy.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-65827-7_4

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DOI: 10.1007/978-3-662-65827-7_4

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