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Financial market equilibria with cumulative prospect theory

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  • De Giorgi, Enrico
  • Hens, Thorsten
  • Rieger, Marc Oliver

Abstract

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a non-negativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents' demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.

Suggested Citation

  • De Giorgi, Enrico & Hens, Thorsten & Rieger, Marc Oliver, 2010. "Financial market equilibria with cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 633-651, September.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:633-651
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    Cited by:

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    2. Matteo Del Vigna, 2011. "Financial market equilibria with heterogeneous agents: CAPM and market segmentation," Working Papers - Mathematical Economics 2011-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    3. Guo, Jing & He, Xue Dong, 2017. "Equilibrium asset pricing with Epstein-Zin and loss-averse investors," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 86-108.
    4. Rabah Amir & Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2022. "An evolutionary finance model with short selling and endogenous asset supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 655-677, April.
    5. Jan Polach & Jiri Kukacka, 2019. "Prospect Theory in the Heterogeneous Agent Model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 147-174, March.
    6. Arvanitis, Stelios & Topaloglou, Nikolas, 2017. "Testing for prospect and Markowitz stochastic dominance efficiency," Journal of Econometrics, Elsevier, vol. 198(2), pages 253-270.
    7. Vicky Henderson, 2012. "Prospect Theory, Liquidation, and the Disposition Effect," Management Science, INFORMS, vol. 58(2), pages 445-460, February.
    8. Bernard, Carole & Ghossoub, Mario, 2009. "Static Portfolio Choice under Cumulative Prospect Theory," MPRA Paper 15446, University Library of Munich, Germany.
    9. Li, Yan & Yang, Liyan, 2013. "Prospect theory, the disposition effect, and asset prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 715-739.
    10. Curatola, Giuliano, 2015. "Loss aversion, habit formation and the term structures of equity and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 103-122.
    11. Matteo Del Vigna, 2011. "Market equilibrium with heterogeneous behavioural and classical investors' preferences," Working Papers - Mathematical Economics 2011-09, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    12. Matteo Del Vigna, 2012. "Stochastic dominance for law invariant preferences: The happy story of elliptical distributions," Working Papers - Mathematical Economics 2012-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    13. Michael J. Best & Robert R. Grauer, 2017. "Humans, Econs and Portfolio Choice," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-30, June.
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    17. Araujo, A. & Gama, J. & Suarez, C.E., 2022. "Lack of prevalence of the endowment effect: An equilibrium analysis," Journal of Mathematical Economics, Elsevier, vol. 102(C).

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    More about this item

    Keywords

    Cumulative prospect theory Prospect theory General equilibrium model Non-convex preferences Continuum of agents;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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