IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v48y2016i4d10.1007_s10614-015-9546-z.html
   My bibliography  Save this article

Fractional Order Financial Models for Awareness and Trial Advertising Decisions

Author

Listed:
  • Benito Chen-Charpentier

    (University of Texas at Arlington)

  • Gilberto González-Parra

    (University of Texas at Arlington
    Universidad de los Andes)

  • Abraham J. Arenas

    (Universidad de Córdoba)

Abstract

Advertising is a type of communication that can be used to encourage, persuade, or manipulate an audience to continue or take some new action. The most common application is to drive consumer behavior with respect to products or services. However, political and ideological advertising has been increasing in the last decades. Different models has been proposed to investigate dynamic advertising problems in business and economics fields. Since the effect of advertising is not instantaneous we present a fractional order model to explain and understand advertising with two components: awareness and trial advertising. In the fractional model the next state depends not only upon its current state but also upon all of its previous states. In order to deal with the fractional derivatives of the model we rely on the Caputo operator and use a predictor-corrector method to numerically approximate the fractional derivatives.

Suggested Citation

  • Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, December.
    • Handle: RePEc:kap:compec:v:48:y:2016:i:4:d:10.1007_s10614-015-9546-z
    DOI: 10.1007/s10614-015-9546-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-015-9546-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-015-9546-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kamrad, Bardia & Lele, Shreevardhan S. & Siddique, Akhtar & Thomas, Robert J., 2005. "Innovation diffusion uncertainty, advertising and pricing policies," European Journal of Operational Research, Elsevier, vol. 164(3), pages 829-850, August.
    2. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    3. Menghan Wang & Qinglong Gou & Chunxu Wu & Liang Liang, 2013. "An aggregate advertising response model based on consumer population dynamics," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 5(1), pages 22-38.
    4. W.H. Ip & K.L. Yung & Dingwei Wang, 2012. "A chaotic model for advertising diffusion problem with competition," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1545-1554.
    5. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    6. Muller, Eitan, 1983. "Trial/awareness advertising decisions : A control problem with phase diagrams with non-stationary boundaries," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 333-350, September.
    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. Sweilam, Nasser H. & Abou Hasan, Muner M. & Baleanu, Dumitru, 2017. "New studies for general fractional financial models of awareness and trial advertising decisions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 772-784.
    2. Rubel, Olivier, 2013. "Stochastic competitive entries and dynamic pricing," European Journal of Operational Research, Elsevier, vol. 231(2), pages 381-392.
    3. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    4. Alina Ferecatu & Arnaud Bruyn & Prithwiraj Mukherjee, 2024. "Silently killing your panelists one email at a time: The true cost of email solicitations," Journal of the Academy of Marketing Science, Springer, vol. 52(4), pages 1216-1239, July.
    5. Mukherjee, Arka & Carvalho, Margarida & Zaccour, Georges, 2023. "Managing quality and pricing during a product recall: An analysis of pre-crisis, crisis and post-crisis regimes," European Journal of Operational Research, Elsevier, vol. 307(1), pages 406-420.
    6. Amini, Mehdi & Wakolbinger, Tina & Racer, Michael & Nejad, Mohammad G., 2012. "Alternative supply chain production–sales policies for new product diffusion: An agent-based modeling and simulation approach," European Journal of Operational Research, Elsevier, vol. 216(2), pages 301-311.
    7. Marc Artzrouni & Patrice Cassagnard, 2017. "Nerlove–Arrow: A New Solution to an Old Problem," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 267-280, January.
    8. Chaab, Jafar & Salhab, Rabih & Zaccour, Georges, 2022. "Dynamic pricing and advertising in the presence of strategic consumers and social contagion: A mean-field game approach," Omega, Elsevier, vol. 109(C).
    9. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    10. Kurt Helmes & Rainer Schlosser, 2015. "Oligopoly Pricing and Advertising in Isoelastic Adoption Models," Dynamic Games and Applications, Springer, vol. 5(3), pages 334-360, September.
    11. Michal Fečkan & JinRong Wang, 2017. "Mixed Order Fractional Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    12. Bryan Bollinger & Kenneth Gillingham & Stefan Lamp & Tsvetan Tsvetanov, 2024. "Promotional Campaign Duration and Word of Mouth in Solar Panel Adoption," Marketing Science, INFORMS, vol. 43(5), pages 1132-1148, September.
    13. den Boer, Arnoud V., 2015. "Tracking the market: Dynamic pricing and learning in a changing environment," European Journal of Operational Research, Elsevier, vol. 247(3), pages 914-927.
    14. Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    15. Pnevmatikos, Nikolaos & Vardar, Baris & Zaccour, Georges, 2018. "When should a retailer invest in brand advertising?," European Journal of Operational Research, Elsevier, vol. 267(2), pages 754-764.
    16. Konstantin Kogan & Avi Herbon & Beatrice Venturi, 2020. "Direct marketing of an event under hazards of customer saturation and forgetting," Annals of Operations Research, Springer, vol. 295(1), pages 207-227, December.
    17. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
    18. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    19. Llibre, Jaume & Valls, Clàudia, 2018. "On the global dynamics of a finance model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 1-4.
    20. Hao Ming & JinRong Wang & Michal Fečkan, 2019. "The Application of Fractional Calculus in Chinese Economic Growth Models," Mathematics, MDPI, vol. 7(8), pages 1-6, July.

    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:kap:compec:v:48:y:2016:i:4:d:10.1007_s10614-015-9546-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.