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Modelling under ambiguity with two correlated Choquet-Brownian motions

Author

Listed:
  • David Roubaud

    (Montpellier Business School, Montpellier Research in Management)

  • Alain Lapied

    (Aix Marseille Univ (Aix-Marseille School of Economics), CNRS & EHESS)

  • Robert Kast

    (CNRS, LAMETA-INRA)

Abstract
Modelling under ambiguity in financial and economic models implies a sound characterisation of ambiguity sources. We expand the seminal work of Kast et al. (2014) who first defined Choquet Random Walks (CRW) and Choquet-Brownian Motions (CBM). Their work allows modelling in the presence of a single source of ambiguity and is used in various contexts, such as investment decisions and portfolio choices. As it is often useful (or even imperative) to introduce multiple sources of ambiguity, we expand the Choquet Brownian model for two correlated sources of ambiguity. Using properties of correlation, we first establish key results for correlated dynamically coherent Choquet Random Walks. We extend it to continuous-time for two correlated sources of ambiguity, each represented by a Choquet-Brownian Motion. Thus, we demonstrate that CBM are sufficiently tractable to adapt to more complex model settings, in the presence of uncertainty represented through two correlated sources of ambiguity. We apply our theoretical model to the optimal portfolio choice of traded assets.

Suggested Citation

  • David Roubaud & Alain Lapied & Robert Kast, 2017. "Modelling under ambiguity with two correlated Choquet-Brownian motions," Economics Bulletin, AccessEcon, vol. 37(2), pages 1012-1020.
    • Handle: RePEc:ebl:ecbull:eb-17-00281
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2017/Volume37/EB-17-V37-I2-P88.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Agliardi, Elettra & Sereno, Luigi, 2011. "The effects of environmental taxes and quotas on the optimal timing of emission reductions under Choquet–Brownian uncertainty," Economic Modelling, Elsevier, vol. 28(6), pages 2793-2802.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, 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. Adkins, Roger & Paxson, Dean, 2011. "Renewing Assets with Uncertain Revenues and Operating Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(3), pages 785-813, June.
    6. David Roubaud & André Lapied & Robert Kast, 2010. "Real Options under Choquet-Brownian Ambiguity," Working Papers halshs-00534027, HAL.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. 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.
    9. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    10. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    11. Elettra Agliardi & Rossella Agliardi & Willem Spanjers, 2015. "Convertible Debt: Financing Decisions and Voluntary Conversion under Ambiguity," International Review of Finance, International Review of Finance Ltd., vol. 15(4), pages 599-611, December.
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    More about this item

    Keywords

    Ambiguity models; Choquet-Brownian Motion; correlated random walk Ambiguity models; Choquet-Brownian Motion; correlated random walk;
    All these keywords.

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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