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Dynamically Consistent Conditional Choquet Capacities

Author

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  • Robert Kast

    ()

  • André Lapied

Abstract

Preferences of a Decision Maker define a valuation function on future uncertain payoffs. Consistency of this unconditional valuation function with valuation conditional on information arrivals is justified by a no Money Pump argument. A result on the updating of capacities is obtained in a static framework. Then the arguments are developed in a model where the future payoffs are contingents on two components: uncertain states and future dates. We obtain results on updating capacities on the uncertain states and “upstating” capacities (discount factors) on future dates in a special case. These results are shown to violate consequentialism.

Suggested Citation

  • Robert Kast & André Lapied, 2007. "Dynamically Consistent Conditional Choquet Capacities," ICER Working Papers - Applied Mathematics Series 20-2007, ICER - International Centre for Economic Research.
  • Handle: RePEc:icr:wpmath:20-2007
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2007/ICERwp20-07.pdf
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    References listed on IDEAS

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    4. Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-1449, November.
    5. Kreps, David M & Porteus, Evan L, 1979. "Dynamic Choice Theory and Dynamic Programming," Econometrica, Econometric Society, vol. 47(1), pages 91-100, January.
    6. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    7. A. Chateauneuf & R. Kast & A. Lapied, 1996. "Choquet Pricing For Financial Markets With Frictions," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 323-330.
    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. Jouini, Elyes & Kallal, Hedi & Napp, Clotilde, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 197-221, April.
    10. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
    11. Ghirardato, Paolo, 1997. "On Independence for Non-Additive Measures, with a Fubini Theorem," Journal of Economic Theory, Elsevier, vol. 73(2), pages 261-291, April.
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    13. repec:dau:papers:123456789/5630 is not listed on IDEAS
    14. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
    15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    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.

    More about this item

    Keywords

    Comonotonicity; Capacities on product spaces; Updating; Flexibilities;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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