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Set-valued star-shaped risk measures

Author

Listed:
  • Bingchu Nie

    (China University of Mining and Technology)

  • Dejian Tian

    (China University of Mining and Technology)

  • Long Jiang

    (China University of Mining and Technology)

Abstract

In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems in the set-valued framework. It is demonstrated that set-valued risk measures can be represented as the union of a family of set-valued convex risk measures, and set-valued normalized star-shaped risk measures can be represented as the union of a family of set-valued normalized convex risk measures. The link between set-valued risk measures and set-valued star-shaped risk measures is also established.

Suggested Citation

  • Bingchu Nie & Dejian Tian & Long Jiang, 2025. "Set-valued star-shaped risk measures," Mathematics and Financial Economics, Springer, volume 19, number 4, October.
    • Handle: RePEc:spr:mathfi:v:19:y:2025:i:2:d:10.1007_s11579-025-00384-4
    DOI: 10.1007/s11579-025-00384-4
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    Keywords

    Set-valued risk measure; Set-valued star-shaped risk measure; Set-valued convex risk measure; Representation theorem;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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