Time consistency conditions for acceptability measures, with an application to tail value at risk

An acceptability measure is a number that summarizes information on monetary outcomes of a given position in various scenarios, and that, depending on context, may be interpreted as a capital requirement or as a price. In a multiperiod setting, it is reasonable to require that an acceptability measure should satisfy certain conditions oftime consistency. Various notions of time consistency may be considered. Within the framework of coherent risk measures as proposed by Artzner et al. (1999), we establish implication relations between a number of different notions, and we determine how eachnotion of time consistency is expressed through properties of a representing set of test measures. We propose modifications of the standard Tail-Value-at-Risk measure that have stronger consistency properties than the original.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.

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