### 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 |

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### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Mathematical Finance*,

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