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Some Stochastic Orders over an Interval with Applications

Author

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  • Lazaros Kanellopoulos

    (Department of Statistics and Insurance Science, University of Piraeus, 80 M. Karaoli & A. Dimitriou Str., 18534 Piraeus, Greece)

Abstract

In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also indicate how these ordering relationships can be adapted to the classical risk model in order to derive a moment bound for ruin probability. Finally, we compare it with other existing bounds.

Suggested Citation

  • Lazaros Kanellopoulos, 2023. "Some Stochastic Orders over an Interval with Applications," Risks, MDPI, vol. 11(9), pages 1-14, September.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:9:p:161-:d:1233350
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    References listed on IDEAS

    as
    1. Cheng, Yu & Pai, Jeffrey S., 2003. "On the nth stop-loss transform order of ruin probability," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 51-60, February.
    2. Psarrakos, Georgios & Politis, Konstadinos, 2008. "Tail bounds for the joint distribution of the surplus prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 163-176, February.
    3. Escudero, Laureano F. & Ortega, Eva-María, 2008. "Actuarial comparisons for aggregate claims with randomly right-truncated claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 255-262, October.
    4. Goovaerts, Marc & De Schepper, Ann, 1997. "IBNR reserves under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 225-244, December.
    5. Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.
    Full references (including those not matched with items on IDEAS)

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