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Supermodular ordering of Poisson arrays

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  • Kızıldemir, Bünyamin
  • Privault, Nicolas

Abstract

We derive necessary and sufficient conditions for the supermodular ordering of certain triangular arrays of Poisson random variables, based on the componentwise ordering of their covariance matrices. Applications are proposed for markets driven by jump–diffusion processes, using sums of Gaussian and Poisson random vectors. Our results rely on a new triangular structure for the representation of Poisson random vectors using their Lévy–Khintchine representation.

Suggested Citation

  • Kızıldemir, Bünyamin & Privault, Nicolas, 2015. "Supermodular ordering of Poisson arrays," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 136-143.
    • Handle: RePEc:eee:stapro:v:98:y:2015:i:c:p:136-143
    DOI: 10.1016/j.spl.2014.12.021
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    References listed on IDEAS

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    1. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Margaret Meyer & Bruno Strulovici, 2013. "Beyond Correlation: Measuring Interdependence Through Complementarities," Economics Series Working Papers 655, University of Oxford, Department of Economics.
    3. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 161-186, February.
    4. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    5. Alfred Müller, 2001. "Stochastic Ordering of Multivariate Normal Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 567-575, September.
    6. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
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    Cited by:

    1. Chung, D. & Linton, O. & Whang Y-J., 2021. "Consistent Testing for an Implication of Supermodular Dominance," Cambridge Working Papers in Economics 2134, Faculty of Economics, University of Cambridge.

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