Details
| Original language | English |
|---|---|
| Pages (from-to) | 413-444 |
| Number of pages | 32 |
| Journal | Mathematics and Financial Economics |
| Volume | 12 |
| Issue number | 3 |
| Publication status | Published - 1 Jun 2018 |
Abstract
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (Stoch Process Appl 126(7):2014–2037, 2016). Further, in analogy to the univariate case in Föllmer (Stat Risk Model 31(1):79–103, 2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.
Keywords
- Conditional certainty equivalents, Law-invariance, Multivariate risk measures, Strong consistency, Systemic risk measures
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Economics, Econometrics and Finance(all)
- Finance
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Mathematics and Financial Economics, Vol. 12, No. 3, 01.06.2018, p. 413-444.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Strongly consistent multivariate conditional risk measures
AU - Hoffmann, Hannes
AU - Meyer-Brandis, Thilo
AU - Svindland, G.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (Stoch Process Appl 126(7):2014–2037, 2016). Further, in analogy to the univariate case in Föllmer (Stat Risk Model 31(1):79–103, 2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.
AB - We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (Stoch Process Appl 126(7):2014–2037, 2016). Further, in analogy to the univariate case in Föllmer (Stat Risk Model 31(1):79–103, 2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.
KW - Conditional certainty equivalents
KW - Law-invariance
KW - Multivariate risk measures
KW - Strong consistency
KW - Systemic risk measures
UR - http://www.scopus.com/inward/record.url?scp=85040321312&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1609.07903
DO - 10.48550/arXiv.1609.07903
M3 - Article
VL - 12
SP - 413
EP - 444
JO - Mathematics and Financial Economics
JF - Mathematics and Financial Economics
SN - 1862-9679
IS - 3
ER -