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Risk aggregation under dependence uncertainty and an order constraint

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  • Chen, Yuyu
  • Lin, Liyuan
  • Wang, Ruodu

Abstract

We study the aggregation of two risks when the marginal distributions are known and the dependence structure is unknown, under the additional constraint that one risk is smaller than or equal to the other. Risk aggregation problems with the order constraint are closely related to the recently introduced notion of the directional lower (DL) coupling. The largest aggregate risk in concave order (thus, the smallest aggregate risk in convex order) is attained by the DL coupling. These results are further generalized to calculate the best-case and worst-case values of tail risk measures. In particular, we obtain analytical formulas for bounds on Value-at-Risk. Our numerical results suggest that the new bounds on risk measures with the extra order constraint can greatly improve those with full dependence uncertainty.

Suggested Citation

  • Chen, Yuyu & Lin, Liyuan & Wang, Ruodu, 2022. "Risk aggregation under dependence uncertainty and an order constraint," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 169-187.
    • Handle: RePEc:eee:insuma:v:102:y:2022:i:c:p:169-187
    DOI: 10.1016/j.insmatheco.2021.10.006
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    More about this item

    Keywords

    Risk aggregation; Risk measures; Value-at-Risk; Concave order; Directional lower coupling;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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