## Abstract

The tail mean-variance model was recently introduced for use in risk management and portfolio choice; it involves a criterion that focuses on the risk of rare but large losses, which is particularly important when losses have heavy-tailed distributions. If returns or losses follow a multivariate elliptical distribution, the use of risk measures that satisfy certain well-known properties is equivalent to risk management in the classical mean-variance framework. The tail mean-variance criterion does not satisfy these properties, however, and the precise optimal solution typically requires the use of numerical methods. We use a convex optimization method and a mean-variance characterization to find an explicit and easily implementable solution for the tail mean-variance model. When a risk-free asset is available, the optimal portfolio is altered in a way that differs from the classical mean-variance setting. A complete solution to the optimal portfolio in the presence of a risk-free asset is also provided.

Original language | English |
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Pages (from-to) | 213-221 |

Number of pages | 9 |

Journal | Insurance: Mathematics and Economics |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2013 |

## Keywords

- Optimal portfolio selection
- Quartic equation
- Tail conditional expectation
- Tail variance

## ASJC Scopus subject areas

- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty