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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
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    References listed on IDEAS

    as
    1. Cheung, Ka Chun, 2007. "Optimal allocation of policy limits and deductibles," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 382-391, November.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Qi Feng & J. George Shanthikumar, 2018. "Arrangement Increasing Resource Allocation," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 935-955, September.
    21. 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.
    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.
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