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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. 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.
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    5. 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.
    6. 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.
    7. Cheung, Ka Chun & Yang, Hailiang, 2004. "Ordering optimal proportions in the asset allocation problem with dependent default risks," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 595-609, December.
    8. 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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    Cited by:

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    3. Wei Wei, 2018. "Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems," Risks, MDPI, vol. 6(2), pages 1-12, April.
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    8. 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.
    9. Wei, Wei, 2017. "Joint stochastic orders of high degrees and their applications in portfolio selections," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 141-148.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Pan, Xiaoqing & Yuan, Min & Kochar, Subhash C., 2015. "Stochastic comparisons of weighted sums of arrangement increasing random variables," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 42-50.
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    18. 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.
    19. 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.
    20. 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.
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    23. 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.

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