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Dynamically consistent Choquet random walk and real investments

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  • Robert Kast

    (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)

  • André Lapied

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

In the real investments literature, the investigated cash flow is assumed to follow some known stochastic process (e.g. Brownian motion) and the criterion to decide between investments is the discounted utility of their cash flows. However, for most new investments the investor may be ambiguous about the representation of uncertainty. In order to take such ambiguity into account, we refer to a discounted Choquet expected utility in our model. In such a setting some problems are to dealt with: dynamical consistency, here it is obtained in a recursive model by a weakened version of the axiom. Mimicking the Brownian motion as the limit of a random walk for the investment payoff process, we describe the latter as a binomial tree with capacities instead of exact probabilities on its branches and show what are its properties at the limit. We show that most results in the real investments literature are tractable in this enlarged setting but leave more room to ambiguity as both the mean and the variance of the underlying stochastic process are modified in our ambiguous model

Suggested Citation

  • Robert Kast & André Lapied, 2010. "Dynamically consistent Choquet random walk and real investments," Working Papers hal-02817702, HAL.
    • Handle: RePEc:hal:wpaper:hal-02817702
    Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-02817702v2
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    References listed on IDEAS

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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. Robert Kast & André Lapied, 2010. "Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty," Theory and Decision, Springer, vol. 69(1), pages 27-53, July.
    3. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330, July.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
    6. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2003. "A Simple Axiomatization of Iterated Choquet Objectives," CIRJE F-Series CIRJE-F-219, CIRJE, Faculty of Economics, University of Tokyo.
    7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    8. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
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    Cited by:

    1. Kast, Robert & Lapied, André & Roubaud, David, 2014. "Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet–Brownian motions," Economic Modelling, Elsevier, vol. 38(C), pages 495-503.
    2. Agliardi, Elettra & Agliardi, Rossella & Spanjers, Willem, 2016. "Corporate financing decisions under ambiguity: Pecking order and liquidity policy implications," Journal of Business Research, Elsevier, vol. 69(12), pages 6012-6020.
    3. Rossella Agliardi, 2017. "Asymmetric Choquet random walks and ambiguity aversion or seeking," Theory and Decision, Springer, vol. 83(4), pages 591-602, December.

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