Topics Related to Gamma Processes

Makoto Yamazato
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Makoto Yamazato: Department of Mathematical Sciences, University of the Ryukyus, Senbaru 1, Nishihara-cho, Okinawa, 903-0213, Japan

Chapter 5 in Stochastic Processes and Applications to Mathematical Finance, 2006, pp 157-182 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThe 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.

Keywords: Stochastic Processes; Mathematical Finance; Malliavin Calculus; Martingale Representation; Chaos Expansion; Levy Processes; Stable Processes; Stochastic Differential Equations; Stochastic Control (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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