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Self-decomposability of weak variance generalised gamma convolutions

Author

Listed:
  • Buchmann, Boris
  • Lu, Kevin W.
  • Madan, Dilip B.

Abstract

Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent processes such as the weak variance alpha–gamma process, and illustrate the necessity of our moment conditions in some cases.

Suggested Citation

  • Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:630-655
    DOI: 10.1016/j.spa.2019.02.012
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    References listed on IDEAS

    as
    1. Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
    2. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
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    6. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
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    Cited by:

    1. Robin Merkle & Andrea Barth, 2022. "On Some Distributional Properties of Subordinated Gaussian Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2661-2688, December.

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