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Increasing quasiconcave co-radiant functions with applications in mathematical economics

Author

Listed:
  • Juan Enrique Martínez-Legaz
  • Alexander M. Rubinov
  • Siegfried Schaible

Abstract

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In particular we identify a small “natural” infimal generator of the set of all coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of production functions and utility functions are discussed. Copyright Springer-Verlag 2005

Suggested Citation

  • Juan Enrique Martínez-Legaz & Alexander M. Rubinov & Siegfried Schaible, 2005. "Increasing quasiconcave co-radiant functions with applications in mathematical economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 261-280, June.
    • Handle: RePEc:spr:mathme:v:61:y:2005:i:2:p:261-280
    DOI: 10.1007/s001860400405
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    Citations

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    Cited by:

    1. Alexander Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series Ec-04/16, European University at St. Petersburg, Department of Economics.
    2. S. Mirzadeh & H. Mohebi, 2016. "Abstract Concavity of Increasing Co-radiant and Quasi-Concave Functions with Applications in Mathematical Economics," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 443-472, May.
    3. Aleksandr G. Alekseev & Mikhail V. Sokolov, 2016. "Benchmark-based evaluation of portfolio performance: a characterization," Annals of Finance, Springer, vol. 12(3), pages 409-440, December.
    4. Ying Gao & Xin-Min Yang, 2019. "Properties of the nonlinear scalar functional and its applications to vector optimization problems," Journal of Global Optimization, Springer, vol. 73(4), pages 869-889, April.
    5. Mynbaev, Kairat, 1998. "Profit Maximization and the Threshold Price," MPRA Paper 20323, University Library of Munich, Germany, revised 29 Jan 2010.
    6. Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.
    7. Aleksandr Alekseev & Mikhail Sokolov, 2016. "Portfolio Return Relative to a Benchmark," EUSP Department of Economics Working Paper Series 2016/04, European University at St. Petersburg, Department of Economics.

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