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Distributions with Heavy Tails in Orlicz Spaces

Author

Listed:
  • Dimitrios G. Konstantinides

    (University of the Aegean)

  • Christos E. Kountzakis

    (University of the Aegean)

Abstract

This paper relies on the application of Kantorovich functionals on quasi-interior points of the positive cone for certain classes of Orlicz spaces. Particularly we provide the asymptotic calculation of the ruin probability in the renewal risk model under heavy-tailed claims in the Orlicz spaces. This application assures the extension of classical asymptotic theory of regular variation.

Suggested Citation

  • Dimitrios G. Konstantinides & Christos E. Kountzakis, 2017. "Distributions with Heavy Tails in Orlicz Spaces," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1726-1762, December.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:4:d:10.1007_s10959-016-0693-5
    DOI: 10.1007/s10959-016-0693-5
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    References listed on IDEAS

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    1. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    2. Haezendonck, J. & Goovaerts, M., 1982. "A new premium calculation principle based on Orlicz norms," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 41-53, January.
    3. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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