Time consistency of dynamic risk measures in markets with transaction costs
AbstractThe paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time consistency of scalar risk measures can be generalized to set-valued risk measures in different ways. The most intuitive generalization is called time consistency. We will show that the equivalence between a recursive form of the risk measure and time consistency, which is a central result in the scalar case, does not hold in the set-valued framework. Instead, we propose an alternative generalization, which we will call multi-portfolio time consistency and show in the main result of the paper that this property is indeed equivalent to the recursive form as well as to an additive property for the acceptance sets. Multi-portfolio time consistency is a stronger property than time consistency. In the scalar case, both notions coincide.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1201.1483.
Date of creation: Jan 2012
Date of revision: Dec 2012
Publication status: Published in Quantitative Finance 13 (9), 1473-1489, (2013)
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-18 (All new papers)
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