Details
| Original language | English |
|---|---|
| Pages (from-to) | 1230-1269 |
| Number of pages | 40 |
| Journal | SIAM Journal on Financial Mathematics |
| Volume | 13 |
| Issue number | 3 |
| Early online date | 22 Sept 2022 |
| Publication status | Published - 2022 |
Abstract
Keywords
- aggregation of random variables in robust models, quasi-sure analysis, Robust mathematical finance, supported uncertainty
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Economics, Econometrics and Finance(all)
- Finance
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Financial Mathematics, Vol. 13, No. 3, 2022, p. 1230-1269.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Model Uncertainty
T2 - A Reverse Approach
AU - Liebrich, Felix Benedikt
AU - Maggis, Marco
AU - Svindland, Gregor
N1 - Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics.
PY - 2022
Y1 - 2022
N2 - In robust finance, Knightian uncertainty is often captured by sets of probability measures on the future states of the world. If these measures are nondominated, this usually comes at the cost of losing tractability, and advanced functional-analytic tools are often not available anymore. This tends to be mitigated by ad hoc assumptions that guarantee a certain degree of tractability, for instance concerning the aggregation of consistent random variables. The present paper instead investigates from a reverse perspective what implications the validity of certain functional-analytic tools has. In this vein, we categorise the Kreps-Yan property, robust variants of the Brannath-Schachermayer Bipolar Theorem and the Grothendieck Lemma, and uncertain volatility models. By doing so, we also uncover connections to robust statistics.
AB - In robust finance, Knightian uncertainty is often captured by sets of probability measures on the future states of the world. If these measures are nondominated, this usually comes at the cost of losing tractability, and advanced functional-analytic tools are often not available anymore. This tends to be mitigated by ad hoc assumptions that guarantee a certain degree of tractability, for instance concerning the aggregation of consistent random variables. The present paper instead investigates from a reverse perspective what implications the validity of certain functional-analytic tools has. In this vein, we categorise the Kreps-Yan property, robust variants of the Brannath-Schachermayer Bipolar Theorem and the Grothendieck Lemma, and uncertain volatility models. By doing so, we also uncover connections to robust statistics.
KW - aggregation of random variables in robust models
KW - quasi-sure analysis
KW - Robust mathematical finance
KW - supported uncertainty
UR - http://www.scopus.com/inward/record.url?scp=85146515345&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2004.06636
DO - 10.48550/arXiv.2004.06636
M3 - Article
VL - 13
SP - 1230
EP - 1269
JO - SIAM Journal on Financial Mathematics
JF - SIAM Journal on Financial Mathematics
SN - 1945-497X
IS - 3
ER -