IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v297y2021i1d10.1007_s10479-020-03770-x.html
   My bibliography  Save this article

On coverage limits and deductibles for SAI loss severities

Author

Listed:
  • Yinping You

    (Huaqiao University)

  • Xiaohu Li

    (Stevens Institute of Technology)

  • Rui Fang

    (Shantou University)

Abstract

This paper studies allocation of coverage limits and deductibles for dependent losses in the frame of utility theory. The optimal allocation of deductibles is derived for SAI losses without frequency impact, and the optimal allocation of coverage limits (deductibles) for SAI loss severities with RWSAI frequencies are proved to be arrayed in ascending (descending) order. Sufficient conditions to exclude the worst allocation of coverage limits are built for comonotonic loss severities with RWSAI frequencies. A real application in house property insurance is presented as well.

Suggested Citation

  • Yinping You & Xiaohu Li & Rui Fang, 2021. "On coverage limits and deductibles for SAI loss severities," Annals of Operations Research, Springer, vol. 297(1), pages 341-357, February.
    • Handle: RePEc:spr:annopr:v:297:y:2021:i:1:d:10.1007_s10479-020-03770-x
    DOI: 10.1007/s10479-020-03770-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03770-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-020-03770-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hua, Lei & Cheung, Ka Chun, 2008. "Stochastic orders of scalar products with applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 865-872, June.
    2. Hua, Lei & Cheung, Ka Chun, 2008. "Worst allocations of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 93-98, August.
    3. Yinping You & Rui Fang & Xiaohu Li, 2016. "Allocating active redundancies to k‐out‐of‐n reliability systems with permutation monotone component lifetimes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 607-620, September.
    4. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    5. Belzunce, Félix & Martínez-Puertas, Helena & Ruiz, José M., 2013. "On allocation of redundant components for systems with dependent components," European Journal of Operational Research, Elsevier, vol. 230(3), pages 573-580.
    6. Zhuang, Weiwei & Chen, Zijin & Hu, Taizhong, 2009. "Optimal allocation of policy limits and deductibles under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 409-414, June.
    7. Cai, Jun & Wei, Wei, 2015. "Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 156-169.
    8. Cai, Jun & Wei, Wei, 2014. "Some new notions of dependence with applications in optimal allocation problems," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 200-209.
    9. Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
    10. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    11. Yinping You & Xiaohu Li, 2014. "On allocating redundancies to k‐out‐of‐ n reliability systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(3), pages 361-371, May.
    12. Li, Chen & Li, Xiaohu, 2017. "Ordering optimal deductible allocations for stochastic arrangement increasing risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 31-40.
    13. Christopher Gaffney & Adi Ben-Israel, 2016. "A simple insurance model: optimal coverage and deductible," Annals of Operations Research, Springer, vol. 237(1), pages 263-279, February.
    14. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    15. Christopher Gaffney & Adi Ben-Israel, 2016. "A simple insurance model: optimal coverage and deductible," Annals of Operations Research, Springer, vol. 237(1), pages 263-279, February.
    16. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    17. You, Yinping & Li, Xiaohu, 2015. "Functional characterizations of bivariate weak SAI with an application," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 225-231.
    18. Li, Xiaohu & You, Yinping, 2012. "On allocation of upper limits and deductibles with dependent frequencies and comonotonic severities," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 423-429.
    19. Franco Pellerey & Saeed Zalzadeh, 2015. "A note on relationships between some univariate stochastic orders and the corresponding joint stochastic orders," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 399-414, May.
    20. Yinping You & Xiaohu Li & Jairo Santanilla, 2017. "Optimal allocations of coverage limits for two independent random losses of insurance policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 497-509, January.
    21. Qi Feng & J. George Shanthikumar, 2018. "Arrangement Increasing Resource Allocation," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 935-955, September.
    22. Lu, ZhiYi & Meng, LiLi, 2011. "Stochastic comparisons for allocations of policy limits and deductibles with applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 338-343, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Yiying & Cheung, Ka Chun, 2020. "On the increasing convex order of generalized aggregation of dependent random variables," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 61-69.
    2. Wei Wei, 2018. "Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems," Risks, MDPI, vol. 6(2), pages 1-12, April.
    3. Cheung, Ka Chun, 2009. "Applications of conditional comonotonicity to some optimization problems," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 89-93, August.
    4. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
    5. Manesh, Sirous Fathi & Khaledi, Baha-Eldin & Dhaene, Jan, 2016. "Optimal allocation of policy deductibles for exchangeable risks," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 87-92.
    6. Pan Xiaoqing & Li Xiaohu, 2017. "On capital allocation for stochastic arrangement increasing actuarial risks," Dependence Modeling, De Gruyter, vol. 5(1), pages 145-153, January.
    7. Li, Chen & Li, Xiaohu, 2020. "Preservation of weak SAI’s under increasing transformations with applications," Statistics & Probability Letters, Elsevier, vol. 164(C).
    8. Yinping You & Xiaohu Li, 2017. "Most unfavorable deductibles and coverage limits for multiple random risks with Archimedean copulas," Annals of Operations Research, Springer, vol. 259(1), pages 485-501, December.
    9. Maria Mercè Claramunt & Maite Màrmol, 2020. "Refundable deductible insurance," Working Papers hal-02909299, HAL.
    10. Cai, Jun & Wei, Wei, 2014. "Some new notions of dependence with applications in optimal allocation problems," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 200-209.
    11. Li, Chen & Li, Xiaohu, 2017. "Ordering optimal deductible allocations for stochastic arrangement increasing risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 31-40.
    12. Yiying Zhang & Weiyong Ding & Peng Zhao, 2018. "On total capacity of k‐out‐of‐n systems with random weights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 347-359, June.
    13. Li, Chen & Li, Xiaohu, 2017. "Preservation of weak stochastic arrangement increasing under fixed time left-censoring," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 42-49.
    14. Qi Feng & J. George Shanthikumar, 2018. "Arrangement Increasing Resource Allocation," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 935-955, September.
    15. Manesh, Sirous Fathi & Khaledi, Baha-Eldin, 2015. "Allocations of policy limits and ordering relations for aggregate remaining claims," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 9-14.
    16. Li, Chen & Li, Xiaohu, 2019. "Preservation of WSAI under default transforms and its application in allocating assets with dependent realizable returns," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 84-91.
    17. Halim Zeghdoudi & Meriem Bouhadjar & Mohamed Riad Remita, 2014. "On Stochastic Orders and its applications : Policy limits and Deductibles," Papers 1411.1609, arXiv.org, revised Jan 2015.
    18. Lu, ZhiYi & Meng, LiLi, 2011. "Stochastic comparisons for allocations of policy limits and deductibles with applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 338-343, May.
    19. Zhang, Yiying & Zhao, Peng, 2015. "Comparisons on aggregate risks from two sets of heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 124-135.
    20. Zhuang, Weiwei & Chen, Zijin & Hu, Taizhong, 2009. "Optimal allocation of policy limits and deductibles under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 409-414, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:297:y:2021:i:1:d:10.1007_s10479-020-03770-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.