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First Passage Times of a Jump Diffusion Process

Mohammadi Oroojeh, Armin | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48908 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohouri Zangeneh, Bijan
  7. Abstract:
  8. In this thesis, we study first passage times of a double exponential jump diffusion process to boundaries. This process consists of a continuous part which includes brownian motion and a jump part with jump sizes which have a double exponential distribution. We study explicit solutions obtained for the laplace transforms, of both the distribution of the first passage times and the joint distribution of the process and its running maxima. Additionally, several interesting probabilistic results are provided. Its results have finance applications, including pricing barrier and lookback options
  9. Keywords:
  10. Levy Process ; Differential Equation ; Integral Equation ; Martingales ; Gaver-Stehfest Algorithm ; Infinitesimal Generator

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