### Abstract

In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics can be used to describe continuity of risk measures. Finally, the methods of probability metrics theory are applied to the benchmark-tracking problem significantly extending the problem setting.

Original language | English |
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Pages (from-to) | 253-277 |

Number of pages | 25 |

Journal | Journal of Statistical Theory and Practice |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - 2008 |

### Keywords

- Benchmark-tracking
- Deviation measure
- Dispersion measure
- Probability metrics
- Risk measure
- Stochastic dominance

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## Cite this

Stoyanov, S. V., Rachev, S. T., & Fabozzi, F. J. (2008). Probability metrics with applications in finance.

*Journal of Statistical Theory and Practice*,*2*(2), 253-277. https://doi.org/10.1080/15598608.2008.10411874