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Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems

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  • Wei Wei

    (Department of Mathematical Sciences, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee, WI 53201, USA)

Abstract

There are extensive studies on the allocation problems in the field of insurance and finance. We observe that these studies, although involving different methodologies, share some inherent commonalities. In this paper, we develop a new framework for these studies with the tool of arrangement increasing functions. This framework unifies many existing studies and provides shortcuts to developing new results.

Suggested Citation

  • Wei Wei, 2018. "Properties of Stochastic Arrangement Increasing and Their Applications in Allocation Problems," Risks, MDPI, vol. 6(2), pages 1-12, April.
  • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:49-:d:143924
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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.
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    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. 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.
    8. 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.
    9. 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.
    10. Masaaki Kijima & Masamitsu Ohnishi, 1996. "Portfolio Selection Problems Via The Bivariate Characterization Of Stochastic Dominance Relations1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 237-277, July.
    11. 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.
    12. 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.
    13. 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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