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A Nonlinear Sandwich Theorem

Author

Listed:
  • Ghossoub Mario

    (Department of Statistics and Actuarial Science, University of Waterloo, Canada;)

  • Principi Giulio

    (Department of Economics, New York University, USA;)

  • Stanca Lorenzo

    (Department of Economics, Social Studies, Applied Mathematics and Statistics (ESOMAS) and Collegio Carlo Alberto, University of Torino, Italy;)

Abstract

We provide a Sandwich Theorem (Konig (1972)) for positively homogeneous functionals that satisfy additivity only on a restricted domain. Our relaxation of additivity is based on a binary relation called convex-conic symmetric preorder, whereby additivity is restricted to all couples of elements that belong to such relation. We then study applications of our nonlinear Sandwich Theorem, proving extension and envelope representation results. Finally, we consider some applications to comonotonicity, a key property in decision theory, risk measurement, and the theory of risk sharing.

Suggested Citation

  • Ghossoub Mario & Principi Giulio & Stanca Lorenzo, 2023. "A Nonlinear Sandwich Theorem," Working papers 081, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    • Handle: RePEc:tur:wpapnw:081
    as

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    File URL: https://www.bemservizi.unito.it/repec/tur/wpapnw/m81.pdf
    File Function: First version, 2023
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    References listed on IDEAS

    as
    1. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    2. Song, Yongsheng & Yan, Jia-An, 2009. "Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 459-465, December.
    3. Ruodu Wang & Yunran Wei & Gordon E. Willmot, 2020. "Characterization, Robustness, and Aggregation of Signed Choquet Integrals," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 993-1015, August.
    4. Denuit, Michel & Dhaene, Jan & Ghossoub, Mario & Robert, Christian Y., 2023. "Comonotonicity and Pareto Optimality, with Application to Collaborative Insurance," LIDAM Discussion Papers ISBA 2023005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Sandwich Theorem; Pataraia's Theorem; C-(super/sub)linearity; convex-conic symmetric preorder.;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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