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Archimedean survival processes

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  • Hoyle, Edward
  • Mengütürk, Levent Ali

Abstract

Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. McNeil and Nešlehová (2009) [12] showed that the class of Archimedean copulas coincides with the class of positive multivariate ℓ1-norm symmetric distributions. Building upon their results, we introduce a class of multivariate Markov processes that we call ‘Archimedean survival processes’ (ASPs). An ASP is defined over a finite time interval, is equivalent in law to a vector of independent gamma processes, and its terminal value has an Archimedean survival copula. There exists a bijection from the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation.

Suggested Citation

  • Hoyle, Edward & Mengütürk, Levent Ali, 2013. "Archimedean survival processes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 1-15.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:1-15
    DOI: 10.1016/j.jmva.2012.09.008
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    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    2. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    3. Hoyle, Edward & Hughston, Lane P. & Macrina, Andrea, 2011. "Lévy random bridges and the modelling of financial information," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 856-884, April.
    4. Norberg, Ragnar, 1999. "Prediction of Outstanding Liabilities II. Model Variations and Extensions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 5-25, May.
    5. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
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    Cited by:

    1. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    2. Mohamed Erraoui & Astrid Hilbert & Mohammed Louriki, 2020. "Bridges with Random Length: Gamma Case," Journal of Theoretical Probability, Springer, vol. 33(2), pages 931-953, June.
    3. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    4. Levent Ali Mengütürk, 2023. "From Irrevocably Modulated Filtrations to Dynamical Equations Over Random Networks," Journal of Theoretical Probability, Springer, vol. 36(2), pages 845-875, June.

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