### Abstract

Original language | English |
---|---|

Pages (from-to) | 428-435 |

Journal | Operations Research |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2019 |

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### Keywords

- F-divergence
- Kullback-Leibler divergence
- heavy tails
- model risk
- robustness

### Cite this

*Operations Research*,

*67*(2), 428-435. https://doi.org/10.1287/opre.2018.1807

}

*Operations Research*, vol. 67, no. 2, pp. 428-435. https://doi.org/10.1287/opre.2018.1807

**The joint impact of F-divergences and reference models on the contents of uncertainty sets.** / Kruse, Thomas; Schneider, Judith C.; Schweizer, Nikolaus.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - 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 - 2019/3

Y1 - 2019/3

N2 - In the presence of model risk, it is well-established to replace classical expected values by 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 which are moderately heavy-tailed such as lognormal models. Worst cases are either infinitely pessimistic, or they 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 by 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 which are moderately heavy-tailed such as lognormal models. Worst cases are either infinitely pessimistic, or they 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 - Kullback-Leibler divergence

KW - heavy tails

KW - model risk

KW - robustness

U2 - 10.1287/opre.2018.1807

DO - 10.1287/opre.2018.1807

M3 - Article

VL - 67

SP - 428

EP - 435

JO - Operations Research

JF - Operations Research

SN - 0030-364X

IS - 2

ER -