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Spectral Representation of Multiply Self-decomposable Stochastic Processes and Applications

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Nguyen Van Thu

    (Department of Mathematics, International University, HCM City, Vietnam)

  • To Anh Dung

    (Department of Mathematics, University of natural sciences, HCM City, Vietnam)

  • Duong Ton Dam

    (Department of Mathematics, University of natural sciences, HCM City, Vietnam)

  • Nguyen Huu Thai

    (Department of Mathematics and Statistics, University of Economics, HCM City, Vietnam)

Abstract

In the present paper we study multiply selfdecomposable probability measures (SDPM) and processes and prove their integral representations. Similarly, the multiple s-selfdecomposability case is treated. Our results extend some of known results due to Urbanik, K., Jurek, Z., Rosinski, J. and Rajput, B.S. As an application, following Cartea and Howinson ([1]) we introduce the Damped-Lévy-mixed - stable process which leads to a mathematical model for option pricing.

Suggested Citation

  • Nguyen Van Thu & To Anh Dung & Duong Ton Dam & Nguyen Huu Thai, 2007. "Spectral Representation of Multiply Self-decomposable Stochastic Processes and Applications," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 245-258, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0015
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