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Integration-segregation decisions under general value functions : "Create your own bundle -- choose 1, 2, or all 3 !"

Author

Listed:
  • Martín Egozcue

    () (Universidad de la República)

  • Sébastien Massoni

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Wing-Keung Wong

    () (HKBU - Hong Kong Baptist University)

  • Ričardas Zitikis

    () (Department of Statistical and Actuarial Sciences - UWO - University of Western Ontario)

Abstract

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance, and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call 'exposure units' to naturally cover manifold scenarios spanning well beyond 'products'. Our findings show, for example, that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e., all are gains) or all negative (i.e., all are losses). In the case of exposure units mixed-sign values, decision rules are much more complex and rely on cataloging the Bell-number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Suggested Citation

  • Martín Egozcue & Sébastien Massoni & Wing-Keung Wong & Ričardas Zitikis, 2012. "Integration-segregation decisions under general value functions : "Create your own bundle -- choose 1, 2, or all 3 !"," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00747008, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00747008
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00747008
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    References listed on IDEAS

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    1. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    2. Heath, Timothy B & Chatterjee, Subimal & France, Karen Russo, 1995. " Mental Accounting and Changes in Price: The Frame Dependence of Reference Dependence," Journal of Consumer Research, Oxford University Press, vol. 22(1), pages 90-97, June.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Richard H. Thaler, 2008. "Mental Accounting and Consumer Choice," Marketing Science, INFORMS, vol. 27(1), pages 15-25, 01-02.
    5. Alexander Ljungqvist & William J. Wilhelm, 2005. "Does Prospect Theory Explain IPO Market Behavior?," Journal of Finance, American Finance Association, vol. 60(4), pages 1759-1790, August.
    6. Egozcue, Martín & García, Luis Fuentes & Wong, Wing-Keung & Zitikis, Ricardas, 2011. "Do investors like to diversify? A study of Markowitz preferences," European Journal of Operational Research, Elsevier, vol. 215(1), pages 188-193, November.
    7. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, October.
    8. Sonya Seongyeon Lim, 2006. "Do Investors Integrate Losses and Segregate Gains? Mental Accounting and Investor Trading Decisions," The Journal of Business, University of Chicago Press, vol. 79(5), pages 2539-2574, September.
    9. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
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    Cited by:

    1. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    2. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.

    More about this item

    Keywords

    Bell number; Bundling; marketing; mental accounting; portfolio theory; value fonction; utility function; majorization; functional inequalities; Bell number.; Package; comptabilité mentale; théorie de portefeuille; fonctions d'utilité; majorisation; inégalités fonctionnelles; nombre de Bell.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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