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On the semimartingale nature of Feller processes with killing

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  • Schnurr, Alexander

Abstract

Let U be an open set in Rd. We show that under a mild assumption on the richness of the generator, a Feller process in (U,B(U)) with (predictable) killing is a semimartingale. To this end, we generalize the notion of semimartingales in a natural way to those ‘with killing’. Furthermore we calculate the semimartingale characteristics of the Feller process explicitly and analyze their connections to the symbol. Finally we derive a probabilistic formula for calculating the symbol of the process.

Suggested Citation

  • Schnurr, Alexander, 2012. "On the semimartingale nature of Feller processes with killing," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2758-2780.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:7:p:2758-2780 DOI: 10.1016/j.spa.2012.04.009
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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    2. Chaumont, L. & Kyprianou, A.E. & Pardo, J.C., 2009. "Some explicit identities associated with positive self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 980-1000, March.
    3. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    4. Fourati, Sonia, 2012. "Explicit solutions of the exit problem for a class of Lévy processes; applications to the pricing of double-barrier options," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1034-1067.
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