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Some new notions of dependence with applications in optimal allocation problems

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  • Cai, Jun
  • Wei, Wei

Abstract

Dependence structures of multiple risks play an important role in optimal allocation problems for insurance, quantitative risk management, and finance. However, in many existing studies on these problems, risks or losses are often assumed to be independent or comonotonic or exchangeable. In this paper, we propose several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks. These characterizations are related to the properties of arrangement increasing functions and the proposed notions of dependence incorporate many typical dependence structures studied in the literature for optimal allocation problems. We also develop the properties of these dependence structures. We illustrate the applications of these notions in the optimal allocation problems of deductibles and policy limits and in capital reserves problems. These applications extend many existing researches to more general dependent risks.

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  • 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.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:200-209
    DOI: 10.1016/j.insmatheco.2014.01.009
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    References listed on IDEAS

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    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. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
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    4. 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.
    5. 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.
    6. 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.
    7. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    8. 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.
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    Cited by:

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    5. 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.
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    8. 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.
    9. 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.
    10. Li, Chen & Li, Xiaohu, 2016. "Sufficient conditions for ordering aggregate heterogeneous random claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 406-413.
    11. Belles-Sampera, Jaume & Guillén, Montserrat & Santolino, Miguel, 2014. "GlueVaR risk measures in capital allocation applications," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 132-137.
    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. 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.
    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. 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.
    16. Rui Fang & Xiaohu Li, 2016. "On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 335-345, June.
    17. 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.
    18. Ju, Shan & Pan, Xiaoqing, 2016. "A new proof for the peakedness of linear combinations of random variables," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 93-98.
    19. Wei Wei, 2018. "Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems," Risks, MDPI, vol. 6(2), pages 1-12, April.
    20. 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.
    21. Belzunce, Félix & Martínez-Riquelme, Carolina, 2023. "A new stochastic dominance criterion for dependent random variables with applications," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 165-176.
    22. 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.
    23. Rui Fang & Xiaohu Li, 2017. "On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 580-598, October.

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