Membership conditions for consistent families of monetary valuations

B. Roorda, J.M. Schumacher

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Abstract

We investigate time consistency of monetary valuations, also called monetary risk measures or monetary utility functions. Through a number of recent research contributions, it has become clear that time consistency imposes strong constraints on families of monetary valuations conditioned on available information at different time instants. In this paper we add to these results by showing that consistent families of monetary valuations are already determined uniquely by the choice of the initial valuation, under suitable sensitivity assumptions; moreover, this statement holds even when the term “consistency” is interpreted in a rather weak sense. The unique update rule is specified explicitly, and we characterize the existence of consistent updates for a given initial monetary valuation. We give examples of situations in which weak consistency is relevant. An application is given to the construction of consistent families of compound valuations, as an illustration of the additional flexibility under weak time consistency.
Original languageEnglish
Pages (from-to)255-280
JournalStatistics & Risk Modeling
Volume30
Issue number3
DOIs
Publication statusPublished - 2013

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Valuation
Time Consistency
Weak Consistency
Update
Risk Measures
Utility Function
Instant
Family
Flexibility
Term
Time consistency

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Roorda, B. ; Schumacher, J.M. / Membership conditions for consistent families of monetary valuations. In: Statistics & Risk Modeling. 2013 ; Vol. 30, No. 3. pp. 255-280.
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Membership conditions for consistent families of monetary valuations. / Roorda, B.; Schumacher, J.M.

In: Statistics & Risk Modeling, Vol. 30, No. 3, 2013, p. 255-280.

Research output: Contribution to journalArticleScientificpeer-review

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