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Dynamically consistent Choquet random walk and real investments

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  • Robert Kast

    ()
    (LAMETA - Laboratoire Montpellierain d'économie théorique et appliquée - CNRS : UMR5474 - INRA : UR1135 - CIHEAM - Université Montpellier I - Montpellier SupAgro)

  • André Lapied

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

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

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00533826.

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Date of creation: 2010
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Handle: RePEc:hal:wpaper:halshs-00533826

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Related research

Keywords: Choquet integrals; conditional Choquet integrals; random walk; Brownian motion; real options; optimal portfolio;

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  1. Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics.
  2. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  3. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  5. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.
  6. Chateauneuf, A. & Kast, R. & Lapied, A., 1992. "Choquet Pricing for Financial Markets with Frictions," G.R.E.Q.A.M. 92a11, Universite Aix-Marseille III.
  7. Robert Kast & André Lapied, 2008. "Valuing future cash flows with non separable discount factors and non additive subjective measures: Conditional Choquet Capacities on Time and on Uncertainty," Working Papers 08-09, LAMETA, Universtiy of Montpellier, revised Jun 2008.
  8. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
  9. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
  10. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
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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.

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