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Applications of conditional comonotonicity to some optimization problems

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  • Cheung, Ka Chun

Abstract

In this article, we study two optimization problems. The first is finding the best L1-approximant of a given random vector on some affine subspaces subject to a measurability condition. The second is finding the optimal allocation of policy limits such that the expected retained loss is minimized. Explicit solutions of both problems are constructed by utilizing the notion of conditional comonotonicity.

Suggested Citation

  • Cheung, Ka Chun, 2009. "Applications of conditional comonotonicity to some optimization problems," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 89-93, August.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:89-93
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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. Elyès Jouini & Clotilde Napp, 2004. "Conditional comonotonicity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 153-166, December.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. 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.
    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. Laeven, Roger J. A. & Goovaerts, Marc J., 2004. "An optimization approach to the dynamic allocation of economic capital," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 299-319, October.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 71-80, May.
    12. Cheung, Ka Chun, 2008. "Improved convex upper bound via conditional comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 651-655, April.
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    Cited by:

    1. Wan-Ni Lai & Yi-Ting Chen & Edward W. Sun, 2021. "Comonotonicity and low volatility effect," Annals of Operations Research, Springer, vol. 299(1), pages 1057-1099, April.
    2. Cheung, K.C. & Rong, Yian & Yam, S.C.P., 2014. "Borch’s Theorem from the perspective of comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 144-151.

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