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Topics Related to Gamma Processes

In: Stochastic Processes And Applications To Mathematical Finance

Author

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  • Makoto Yamazato

    (Department of Mathematical Sciences, University of the Ryukyus, Senbaru 1, Nishihara-cho, Okinawa, 903-0213, Japan)

Abstract

The aim of this paper is to explain important but not popular properties related to gamma processes and show the applicability of these properties. We define subclasses (CME and its subclasses) of the class of infinitely divisible distributions, which are generated by mixtures and convolutions from gamma distributions, and study their properties. Then we apply the obtained results to the uni-modality of the distributions in the above classes, the boundedness in space-time parameters of transition densities of subordinators generated by CME distributions and the determination of the class of hitting time distributions of 1-dimensional generalized diffusion processes. Finally, we remark that some subclasses of the class CME and the class of selfdecomposable distributions are often used in mathematical finance.

Suggested Citation

  • Makoto Yamazato, 2006. "Topics Related to Gamma Processes," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 5, pages 157-182, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812774637_0005
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    Cited by:

    1. Jirô Akahori & Takahiro Tsuchiya, 2006. "What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 299-313, December.
    2. Hayashi, Masafumi & Takeuchi, Atsushi & Yamazato, Makoto, 2024. "Space-time boundedness and asymptotic behaviors of the densities of CME-subordinators," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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