IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-02433422.html
   My bibliography  Save this paper

Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement

Author

Listed:
  • Christian Deffo Tassak

    (UY1 - Université de Yaoundé I)

  • Louis Aimé Fono

    (Université de Douala)

  • Jules Sadefo-Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, UG - Université de Guyane, MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

Abstract

A more general concept of risk in economics consists on the chance of getting an income or a return less than a threshold one. Risk has been studied and generalized more earlier by Fishburn [8] through Mean Partial Lower Moment specially when income can be described by a random variable. In this paper, we present a new concept of partial moment, namely Fuzzy Lower Partial Moment (FLPM) based on credibility measure, to quantify risk of getting a return described by a fuzzy variable and we study its properties. Based on FLPM, we introduce mean risk dominance for fuzzy variables, we characterize the dominance for some specific cases and we determine some of its properties. Furthermore, we study the consistency of mean-risk models with respect to first and second order dominances. We display one application of FLPM by introducing a new poverty index for poverty measurement in the context of fuzzy environment and we examine some of its properties.

Suggested Citation

  • Christian Deffo Tassak & Louis Aimé Fono & Jules Sadefo-Kamdem, 2019. "Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement," Working Papers hal-02433422, HAL.
    • Handle: RePEc:hal:wpaper:hal-02433422
    Note: View the original document on HAL open archive server: https://hal.umontpellier.fr/hal-02433422
    as

    Download full text from publisher

    File URL: https://hal.umontpellier.fr/hal-02433422/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono & Nicolas Gabriel Andjiga, 2017. "Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1491-1502, December.
    2. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    3. Achille Lemmi & Gianni Betti (ed.), 2006. "Fuzzy Set Approach to Multidimensional Poverty Measurement," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-34251-1, July.
    4. Satya R. Chakravarty, 2019. "An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 123-141, Springer.
    5. Hagenaars, Aldi J M, 1987. "A Class of Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 583-607, October.
    6. repec:bla:jecsur:v:11:y:1997:i:2:p:123-62 is not listed on IDEAS
    7. Sadefo Kamdem, Jules & Tassak Deffo, Christian & Fono, Louis Aimé, 2012. "Moments and semi-moments for fuzzy portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 517-530.
    8. Mauricio Gallardo, 2018. "Identifying Vulnerability To Poverty: A Critical Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1074-1105, September.
    9. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    10. Mozaffar Qizilbash, 2006. "Philosophical Accounts of Vagueness, Fuzzy Poverty Measures and Multidimensionality," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Achille Lemmi & Gianni Betti (ed.), Fuzzy Set Approach to Multidimensional Poverty Measurement, chapter 1, pages 9-28, Springer.
    11. S. M. Sunoj & S. S. Maya, 2008. "The role of lower partial moments in stochastic modeling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 223-242.
    12. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sen, Sugata, 2019. "Decomposition of intra-household disparity sensitive fuzzy multi-dimensional poverty index: A study of vulnerability through Machine Learning," MPRA Paper 93550, University Library of Munich, Germany.
    2. Paolo Giordani & Giovanni Giorgi, 2010. "A fuzzy logic approach to poverty analysis based on the Gini and Bonferroni inequality indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 587-607, November.
    3. Buhong Zheng, 2015. "Poverty: fuzzy measurement and crisp ordering," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 203-229, June.
    4. Espinoza-Delgado, José & Silber, Jacques, 2018. "Multi-dimensional poverty among adults in Central America and gender differences in the three I’s of poverty: Applying inequality sensitive poverty measures with ordinal variables," MPRA Paper 88750, University Library of Munich, Germany.
    5. Maki Michinaka & Takahiro Ito, 2010. "Multidimensional Poverty Rankings based on Pareto Principle: A Practical Extension," Global COE Hi-Stat Discussion Paper Series gd10-139, Institute of Economic Research, Hitotsubashi University.
    6. S. M. Sunoj & S. S. Maya, 2008. "The role of lower partial moments in stochastic modeling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 223-242.
    7. Valérie Berenger & Cuauhtémoc Calderón Villarreal & Franck Celestini, 2009. "Modelling the Distribution of Multidimensional Poverty Scores: Evidence from Mexico," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 24(1), pages 3-34.
    8. Flores, Gabriela & O’Donnell, Owen, 2016. "Catastrophic medical expenditure risk," Journal of Health Economics, Elsevier, vol. 46(C), pages 1-15.
    9. Burhan Can Karahasan & Fırat Bilgel, 2021. "The Topography and Sources of Multidimensional Poverty in Turkey," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 154(2), pages 413-445, April.
    10. Dipesh Gangopadhyay & Robert B. Nielsen & Velma Zahirovic-Herbert, 2021. "Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 1-37, January.
    11. Breitmeyer, Carsten & Hakenes, Hendrik & Pfingsten, Andreas, 2004. "From poverty measurement to the measurement of downside risk," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 327-348, May.
    12. Anh Thu Quang Pham & Pundarik Mukhopadhaya & Ha Vu, 2021. "Estimating poverty and vulnerability to monetary and non-monetary poverty: the case of Vietnam," Empirical Economics, Springer, vol. 61(6), pages 3125-3177, December.
    13. Christian Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
    14. Sandip Sarkar & Manoranjan Pal, 2018. "On the Estimation of Lower and Upper Bounds of Poverty Line: An Illustration with Indian Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 901-924, August.
    15. Dalila De Rosa, 2018. "Capability Approach and Multidimensional Well-Being: The Italian Case of BES," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 140(1), pages 125-155, November.
    16. Wang, Qiong & Mukhopadhaya, Pundarik & Ye, Jingyi, 2020. "An evaluation of the changes in wellbeing in China – 2005 to 2015: An exploratory study," China Economic Review, Elsevier, vol. 61(C).
    17. Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2016. "Efficient skewness/semivariance portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 17(5), pages 331-346, September.
    18. Elie Matta & Jean McGuire, 2008. "Too Risky to Hold? The Effect of Downside Risk, Accumulated Equity Wealth, and Firm Performance on CEO Equity Reduction," Organization Science, INFORMS, vol. 19(4), pages 567-580, August.
    19. Belhadj, Besma & Limam, Mohamed, 2012. "Unidimensional and multidimensional fuzzy poverty measures: New approach," Economic Modelling, Elsevier, vol. 29(4), pages 995-1002.
    20. Duclos, Jean-Yves & Araar, Abdelkrim & Giles, John, 2010. "Chronic and transient poverty: Measurement and estimation, with evidence from China," Journal of Development Economics, Elsevier, vol. 91(2), pages 266-277, March.

    More about this item

    Keywords

    Credibility measure; Fuzzy variable; Fuzzy lower partial mo-ment; Mean-Risk dominance; Poverty index;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-02433422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.