### Abstract

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy or another f-divergence or Bregman distance. We use the theory of minimizing convex integral functionals under moment constraints to give formulae for the calculation of distribution model risk and to explicitly determine the worst case distribution from the set of plausible distributions. We also evaluate related risk measures describing divergence preferences.

Original language | English |
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Pages (from-to) | 395-411 |

Number of pages | 17 |

Journal | Mathematical Finance |

Volume | 26 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2016 |

### Fingerprint

### Keywords

- Bregman distance
- Convex integral functional
- Divergence preferences
- f-divergence
- Generalized exponential family
- Maximum entropy principle
- Multiple priors
- Relative entropy

### ASJC Scopus subject areas

- Applied Mathematics
- Finance
- Accounting
- Economics and Econometrics
- Social Sciences (miscellaneous)

### Cite this

*Mathematical Finance*,

*26*(2), 395-411. https://doi.org/10.1111/mafi.12050

**Measuring distribution model risk.** / Breuer, Thomas; Csiszár, I.

Research output: Contribution to journal › Article

*Mathematical Finance*, vol. 26, no. 2, pp. 395-411. https://doi.org/10.1111/mafi.12050

}

TY - JOUR

T1 - Measuring distribution model risk

AU - Breuer, Thomas

AU - Csiszár, I.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy or another f-divergence or Bregman distance. We use the theory of minimizing convex integral functionals under moment constraints to give formulae for the calculation of distribution model risk and to explicitly determine the worst case distribution from the set of plausible distributions. We also evaluate related risk measures describing divergence preferences.

AB - We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy or another f-divergence or Bregman distance. We use the theory of minimizing convex integral functionals under moment constraints to give formulae for the calculation of distribution model risk and to explicitly determine the worst case distribution from the set of plausible distributions. We also evaluate related risk measures describing divergence preferences.

KW - Bregman distance

KW - Convex integral functional

KW - Divergence preferences

KW - f-divergence

KW - Generalized exponential family

KW - Maximum entropy principle

KW - Multiple priors

KW - Relative entropy

UR - http://www.scopus.com/inward/record.url?scp=84960084060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960084060&partnerID=8YFLogxK

U2 - 10.1111/mafi.12050

DO - 10.1111/mafi.12050

M3 - Article

VL - 26

SP - 395

EP - 411

JO - Mathematical Finance

JF - Mathematical Finance

SN - 0960-1627

IS - 2

ER -