Details
| Original language | English |
|---|---|
| Pages (from-to) | 428-435 |
| Number of pages | 8 |
| Journal | Operations research |
| Volume | 67 |
| Issue number | 2 |
| Early online date | 29 Mar 2019 |
| Publication status | Published - Apr 2019 |
| Externally published | Yes |
Abstract
In the presence of model risk, it is well established to replace classical expected values with worst-case expectations over all models within a fixed radius from a given reference model. This is the “robustness” approach. For the class of F-divergences, we provide a careful assessment of how the interplay between reference model and divergence measure shapes the contents of uncertainty sets. We show that the classical divergences, relative entropy and polynomial divergences, are inadequate for reference models that are moderately heavy-tailed, such as lognormal models. Worst cases either are infinitely pessimistic or rule out the possibility of fat-tailed “power law” models as plausible alternatives. Moreover, we rule out the existence of a single F-divergence, which is appropriate regardless of the reference model. Thus, the reference model should not be neglected when settling on any particular divergence measure in the robustness approach.
Keywords
- F-divergence, Heavy tails, Kullback–Leibler divergence, Model risk, Robustness
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Decision Sciences(all)
- Management Science and Operations Research
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In: Operations research, Vol. 67, No. 2, 04.2019, p. 428-435.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Technical Note—The Joint Impact of F-Divergences and Reference Models on the Contents of Uncertainty Sets
AU - Kruse, Thomas
AU - Schneider, Judith C.
AU - Schweizer, Nikolaus
PY - 2019/4
Y1 - 2019/4
N2 - In the presence of model risk, it is well established to replace classical expected values with worst-case expectations over all models within a fixed radius from a given reference model. This is the “robustness” approach. For the class of F-divergences, we provide a careful assessment of how the interplay between reference model and divergence measure shapes the contents of uncertainty sets. We show that the classical divergences, relative entropy and polynomial divergences, are inadequate for reference models that are moderately heavy-tailed, such as lognormal models. Worst cases either are infinitely pessimistic or rule out the possibility of fat-tailed “power law” models as plausible alternatives. Moreover, we rule out the existence of a single F-divergence, which is appropriate regardless of the reference model. Thus, the reference model should not be neglected when settling on any particular divergence measure in the robustness approach.
AB - In the presence of model risk, it is well established to replace classical expected values with worst-case expectations over all models within a fixed radius from a given reference model. This is the “robustness” approach. For the class of F-divergences, we provide a careful assessment of how the interplay between reference model and divergence measure shapes the contents of uncertainty sets. We show that the classical divergences, relative entropy and polynomial divergences, are inadequate for reference models that are moderately heavy-tailed, such as lognormal models. Worst cases either are infinitely pessimistic or rule out the possibility of fat-tailed “power law” models as plausible alternatives. Moreover, we rule out the existence of a single F-divergence, which is appropriate regardless of the reference model. Thus, the reference model should not be neglected when settling on any particular divergence measure in the robustness approach.
KW - F-divergence
KW - Heavy tails
KW - Kullback–Leibler divergence
KW - Model risk
KW - Robustness
UR - http://www.scopus.com/inward/record.url?scp=85068468799&partnerID=8YFLogxK
U2 - 10.1287/opre.2018.1807
DO - 10.1287/opre.2018.1807
M3 - Article
AN - SCOPUS:85068468799
VL - 67
SP - 428
EP - 435
JO - Operations research
JF - Operations research
SN - 0030-364X
IS - 2
ER -