### Abstract

We define decreasing higher-degree Ross risk aversion and provide an intuitive interpretation for it. We show that all deteriorations of background risk in the sense of n -th risk increase raise risk aversion in the Arrow-Pratt sense if and only if decreasing ( n + 1 ) -th degree Ross risk aversion holds. Meanwhile, the utility functional form of the agent with decreasing ( n + 1 ) -th degree Ross risk aversion is specified. Our result also implies decreasing 3-rd degree Ross risk aversion can be used to characterize the sufficient condition of risk vulnerability. Moreover, our analysis shows the implication of decreasing n / m -th ( n > m ≥ 1 ) Ross risk aversion.

Original language | English |
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Pages (from-to) | 136-142 |

Number of pages | 7 |

Journal | Journal of Mathematical Economics |

Volume | 55 |

Early online date | 26 Feb 2014 |

DOIs | |

Publication status | Published - Dec 2014 |

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### Bibliographical note

This research was supported by the Faculty Research Grant of Lingnan University under Research Project No. DR12A9, Direct Grant for Research of Lingnan University under Research Project No. DR13C8 and the Fundamental Research Funds for the Central Universities under Research Project No. NR2014002.### Keywords

- Background risk
- Decreasing n-th Ross risk aversion
- Risk vulnerability: one-switch utility function