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Weakly time consistent concave valuations and their dual representations

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  • Berend Roorda
  • Johannes Schumacher

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

Suggested Citation

  • Berend Roorda & Johannes Schumacher, 2016. "Weakly time consistent concave valuations and their dual representations," Finance and Stochastics, Springer, vol. 20(1), pages 123-151, January.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:1:p:123-151
    DOI: 10.1007/s00780-015-0285-8
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    Cited by:

    1. 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.
    2. 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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    More about this item

    Keywords

    Convex risk measures; Concave valuations; Duality; Weak time consistency; Risk aversion; 91B30; 91G99; 46A20; 46N10; D81; C61; G28; G22;
    All these keywords.

    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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