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On inverse-Gamma distribution delayed by Poisson process

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  • Bareche, Aîcha
  • Bibi, Abdelouahab

Abstract

The models of stochastic subordination, or random time indexing, has been recently applied to model financial returns series X(t)t≥0 exhibiting sharp, and large variations. These sharp and large variations are linked to information arrivals and/or represent sudden events, and hence we have a model with jumps. For this purpose, by substituting the usual deterministic time t as a subordinator T(t)t≥0 in a stochastic process X(t)t≥0 we obtain a new process X(T(t))t≥0 whose stochastic time is dominated by the subordinator T(t)t≥0. Therefore, we propose in this paper an alternative approach based on a combination of the continuous-time bilinear (COBL) process subordinated by a Poisson process (that it is a Levy process) which permits us to introduce further randomness for the phenomena which exhibit either a speeded up or slowed down behavior. So, the main probabilistic properties of such models are studied and the explicit expression of the higher-order moments properties are given.

Suggested Citation

  • Bareche, Aîcha & Bibi, Abdelouahab, 2023. "On inverse-Gamma distribution delayed by Poisson process," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715223000111
    DOI: 10.1016/j.spl.2023.109787
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    References listed on IDEAS

    as
    1. Abdelouahab Bibi & Fateh Merahi, 2020. "Yule-Walker type estimator of first-order time-varying periodic bilinear differential model for stochastic processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(16), pages 4046-4072, August.
    2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    3. Kei Kobayashi, 2011. "Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 24(3), pages 789-820, September.
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