## Abstract

It is well-known that if a random vector with given marginal distributions is comonotonic, it has the

largest sum with respect to convex order. However, replacing the (unknown) copula by the comonotonic

copula will in most cases not reflect reality well. For instance, in an insurance context we may have

partial information about the dependence structure of different risks in the lower tail. In this paper, we

extend the aforementioned result, using the concept of upper comonotonicity, to the case where the

dependence structure of a random vector in the lower tail is already known. Since upper comonotonic

random vectors have comonotonic behavior in the upper tail, we are able to extend several well-known

results of comonotonicity to upper comonotonicity. As an application, we construct different increasing

convex upper bounds for sums of random variables and compare these bounds in terms of increasing

convex order

largest sum with respect to convex order. However, replacing the (unknown) copula by the comonotonic

copula will in most cases not reflect reality well. For instance, in an insurance context we may have

partial information about the dependence structure of different risks in the lower tail. In this paper, we

extend the aforementioned result, using the concept of upper comonotonicity, to the case where the

dependence structure of a random vector in the lower tail is already known. Since upper comonotonic

random vectors have comonotonic behavior in the upper tail, we are able to extend several well-known

results of comonotonicity to upper comonotonicity. As an application, we construct different increasing

convex upper bounds for sums of random variables and compare these bounds in terms of increasing

convex order

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

Pages (from-to) | 159-166 |

Journal | Insurance: Mathematics and Economics |

Volume | 47 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |