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Risk reducers in convex order

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  • He, Junnan
  • Tang, Qihe
  • Zhang, Huan

Abstract

Given a risk position X, a random addition Z is called a risk reducer for X if the new position X+Z is less risky than X+E[Z] in convex order. We utilize the concept of convex hull to give a structural description of risk reducers in the case of an atomless probability space. Then we study risk reducers that are fully dependent on X. Applications to multivariate stochastic ordering, index-linked hedging strategies, and optimal reinsurance are proposed.

Suggested Citation

  • He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:80-88
    DOI: 10.1016/j.insmatheco.2016.05.009
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    Cited by:

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    3. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures," Papers 2412.00655, arXiv.org.
    4. Liu, Jing, 2018. "LLN-type approximations for large portfolio losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 71-77.

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    More about this item

    Keywords

    Convex hull; Co/counter-monotonicity; Multivariate stochastic ordering; Index-linked hedging strategies; Optimal reinsurance;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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