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Weakly time consistent concave valuations and their dual representations

Author

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  • Roorda, B.
  • Schumacher, Hans

    (Tilburg University, School of Economics and Management)

Abstract

We derive dual characterizations of two notions of weak time consistency for concave valuations, which are convex risk measures under a positive sign convention. Combined with a suitable risk aversion property, these notions are shown to amount to three simple rules for not necessarily minimal representations, describing precisely which features of a valuation determine its unique consistent update. A compatibility result shows that for a time-indexed sequence of valuations, it is sufficient to verify these rules only pairwise with respect to the initial valuation, or in discrete time, only stepwise. We conclude by describing classes of consistently risk averse dynamic valuations with prescribed static properties per time step. This gives rise to a new formalism for recursive valuation. Copyright The Author(s) 2016
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Roorda, B. & Schumacher, Hans, 2016. "Weakly time consistent concave valuations and their dual representations," Other publications TiSEM 132bdd0b-40dd-44bd-ab64-c, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:132bdd0b-40dd-44bd-ab64-cea369c8b81e
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    References listed on IDEAS

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    4. Roorda Berend & Schumacher Hans, 2013. "Membership conditions for consistent families of monetary valuations," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 255-280, August.
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    Cited by:

    1. Roorda Berend & Schumacher Hans, 2013. "Membership conditions for consistent families of monetary valuations," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 255-280, August.
    2. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2019. "Time-consistency of risk measures: how strong is such a property?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 287-317, June.

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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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