IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0294.html
   My bibliography  Save this article

Estimating the means and the covariances of fuzzy random variables

Author

Listed:
  • Shvedov, Alexey

    (National Research University Higher School of Economics, Moscow, Russian Federation)

Abstract

At present, methods of fuzzy mathematics are applied in different fields. For example, fuzzy numbers can be used to model returns of assets in portfolio selection problem when historical data is unavailable. While for other assets possibility of using random variables should be kept. This paper presents new estimators of the means and the covariances of fuzzy random variables. Unbiasedness and consistency of these estimators are established.

Suggested Citation

  • Shvedov, Alexey, 2016. "Estimating the means and the covariances of fuzzy random variables," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 121-138.
    • Handle: RePEc:ris:apltrx:0294
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2016_42_121-138.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.
    2. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Shapiro, A.F. & Terraza, M., 2014. "CAPM with fuzzy returns and hypothesis testing," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 40-57.
    3. Fang, Yong & Lai, K.K. & Wang, Shou-Yang, 2006. "Portfolio rebalancing model with transaction costs based on fuzzy decision theory," European Journal of Operational Research, Elsevier, vol. 175(2), pages 879-893, December.
    4. Wu, Hsien-Chung, 2003. "The fuzzy estimators of fuzzy parameters based on fuzzy random variables," European Journal of Operational Research, Elsevier, vol. 146(1), pages 101-114, April.
    5. Huang, Xiaoxia, 2007. "Two new models for portfolio selection with stochastic returns taking fuzzy information," European Journal of Operational Research, Elsevier, vol. 180(1), pages 396-405, July.
    6. Dabuxilatu Wang, 2004. "A note on consistency and unbiasedness of point estimation with fuzzy data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 93-104, July.
    7. K. Thiagarajah & A. Thavaneswaran, 2006. "Fuzzy random-coefficient volatility models with financial applications," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 503-524, November.
    8. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    9. Liu, Fan-Yong, 2009. "Pricing currency options based on fuzzy techniques," European Journal of Operational Research, Elsevier, vol. 193(2), pages 530-540, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Brychykova, A., 2019. "Capital Asset Pricing Model Using Fuzzy Data and Application for the Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 43(3), pages 58-77.

    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. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    2. Gholamreza Hesamian & Jalal Chachi, 2015. "Two-sample Kolmogorov–Smirnov fuzzy test for fuzzy random variables," Statistical Papers, Springer, vol. 56(1), pages 61-82, February.
    3. Li, Jun & Xu, Jiuping, 2009. "A novel portfolio selection model in a hybrid uncertain environment," Omega, Elsevier, vol. 37(2), pages 439-449, April.
    4. Gupta, Pankaj & Mittal, Garima & Mehlawat, Mukesh Kumar, 2013. "Expected value multiobjective portfolio rebalancing model with fuzzy parameters," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 190-203.
    5. Liu, Yong-Jun & Zhang, Wei-Guo, 2015. "A multi-period fuzzy portfolio optimization model with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 242(3), pages 933-941.
    6. Yong-Jun Liu & Wei-Guo Zhang, 2018. "Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 941-968, May.
    7. Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    8. Takashi Hasuike & Mukesh Kumar Mehlawat, 2018. "Investor-friendly and robust portfolio selection model integrating forecasts for financial tendency and risk-averse," Annals of Operations Research, Springer, vol. 269(1), pages 205-221, October.
    9. Zhang, Wei-Guo & Liu, Yong-Jun & Xu, Wei-Jun, 2012. "A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 222(2), pages 341-349.
    10. Pedro Antonio Martín-Cervantes & María del Carmen Valls Martínez, 2023. "Unraveling the relationship between betas and ESG scores through the Random Forests methodology," Risk Management, Palgrave Macmillan, vol. 25(3), pages 1-29, September.
    11. Hasuike, Takashi & Ishii, Hiroaki, 2009. "On flexible product-mix decision problems under randomness and fuzziness," Omega, Elsevier, vol. 37(4), pages 770-787, August.
    12. de Andrés-Sánchez, Jorge & González-Vila Puchades, Laura, 2017. "The valuation of life contingencies: A symmetrical triangular fuzzy approximation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 83-94.
    13. Krzysztof Piasecki & Joanna Siwek, 2018. "The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 57-74.
    14. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    15. Zhao, Daping & Bai, Lin & Fang, Yong & Wang, Shouyang, 2022. "Multi‐period portfolio selection with investor views based on scenario tree," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    16. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
    17. Ravi Shankar Kumar & M. K. Tiwari & A. Goswami, 2016. "Two-echelon fuzzy stochastic supply chain for the manufacturer–buyer integrated production–inventory system," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 875-888, August.
    18. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2017. "Fuzzy Logic-based Portfolio Selection with Particle Filtering and Anomaly Detection," CIRJE F-Series CIRJE-F-1037, CIRJE, Faculty of Economics, University of Tokyo.
    19. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2017. "Creating Investment Scheme with State Space Modeling ," CIRJE F-Series CIRJE-F-1038, CIRJE, Faculty of Economics, University of Tokyo.
    20. John Dairo Ramirez Aristizabal & Eduardo Alexander Duque Grisales, 2016. "Design Of A Investment Portfolio Using Non-Linear Programming: Case Of Colombia 2013-2014, Diseno De Un Portafolio De Inversion A Partir De Un Modelo De Programacion No Lineal: Caso Colombia 2013-2014," Revista Internacional Administracion & Finanzas, The Institute for Business and Finance Research, vol. 9(2), pages 31-47.

    More about this item

    Keywords

    fuzzy data analysis; fuzzy random variables; point estimation; unbiasedness; consistency;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:ris:apltrx:0294. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

    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: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.