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Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall–Olkin law

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  • Brigo, Damiano
  • Mai, Jan-Frederik
  • Scherer, Matthias

Abstract

A new characterization of the Marshall–Olkin distribution is provided: all sub-vectors of the associated survival indicators are continuous-time Markov chains. This property is crucial to overcome practical limitations for the modeling of high-dimensional default times (rebalancing, iterative simulation, consistent sub-portfolios).

Suggested Citation

  • Brigo, Damiano & Mai, Jan-Frederik & Scherer, Matthias, 2016. "Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall–Olkin law," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 60-66.
    • Handle: RePEc:eee:stapro:v:114:y:2016:i:c:p:60-66
    DOI: 10.1016/j.spl.2016.03.013
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    References listed on IDEAS

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    1. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    2. Fan Yu, 2007. "Correlated Defaults In Intensity‐Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173, April.
    3. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    4. Bladt, Mogens, 2005. "A Review on Phase-type Distributions and their Use in Risk Theory," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 145-161, May.
    5. David Assaf & Naftali A. Langberg & Thomas H. Savits & Moshe Shaked, 1984. "Multivariate Phase-Type Distributions," Operations Research, INFORMS, vol. 32(3), pages 688-702, June.
    6. Damiano Brigo & Kyriakos Chourdakis, 2012. "Consistent single- and multi-step sampling of multivariate arrival times: A characterization of self-chaining copulas," Papers 1204.2090, arXiv.org, revised Apr 2012.
    7. Mai, Jan-Frederik & Scherer, Matthias, 2012. "H-extendible copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 151-160.
    8. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    9. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2007. "Cluster-Based Extension Of The Generalized Poisson Loss Dynamics And Consistency With Single Names," World Scientific Book Chapters, in: Alexander Lipton & Andrew Rennie (ed.), Credit Correlation Life After Copulas, chapter 2, pages 15-39, World Scientific Publishing Co. Pte. Ltd..
    10. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
    11. Damiano Brigo & Jan-Frederik Mai & Matthias Scherer, 2013. "Consistent iterated simulation of multi-variate default times: a Markovian indicators characterization," Papers 1306.0887, arXiv.org, revised May 2014.
    12. Marshall, A. W. & Olkin, I., 1995. "Multivariate Exponential and Geometric Distributions with Limited Memory," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 110-125, April.
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    Cited by:

    1. Sloot Henrik, 2022. "Implementing Markovian models for extendible Marshall–Olkin distributions," Dependence Modeling, De Gruyter, vol. 10(1), pages 308-343, January.

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