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Dynamically consistent Choquet random walk and real investments

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  • André Lapied
  • Robert Kast

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

  • André Lapied & Robert Kast, 2010. "Dynamically consistent Choquet random walk and real investments," Working Papers 10-21, LAMETA, Universtiy of Montpellier, revised 2010.
    • Handle: RePEc:lam:wpaper:10-21
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    File URL: http://www.lameta.univ-montp1.fr/Documents/DR2010-21.pdf
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    References listed on IDEAS

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    1. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    2. 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.
    3. 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.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. 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.
    6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    7. 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.
    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. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    10. repec:dau:papers:123456789/5630 is not listed on IDEAS
    11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    12. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
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    Cited by:

    1. 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.
    2. E. Agliardi & R. Agliardi & W. Spanjers, 2014. "Cash holdings and financing decisions under ambiguity," Working Papers wp979, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Rossella Agliardi, 2017. "Asymmetric Choquet random walks and ambiguity aversion or seeking," Theory and Decision, Springer, vol. 83(4), pages 591-602, December.
    4. 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.
    5. Rossella Agliardi, 2018. "Value-at-risk under ambiguity aversion," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 4(1), pages 1-13, December.

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