Dynamic monetary risk measures for bounded discrete-time processes

Details Dynamic monetary risk measures for bounded discrete-time processes Dynamic monetary risk measures for bounded discrete-time processes

2004-10-21

arxiv.org/abs/math/0410453v1

Mathematics

Probability

41 pages

Scientific paper

We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time, and we show how this property manifests itself in the corresponding process of acceptance sets. For processes of coherent and convex monetary risk measures admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals.

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