Li, Minqiang
(2014):
*Aumann and Serrano's Economic Index of Risk for Sums of Gambles.*

Preview |
PDF
MPRA_paper_55697.pdf Download (63kB) | Preview |

## Abstract

We study Aumann and Serrano's (2008) risk index for sums of gambles that are not necessarily independent. We show that if the dependent parts of two gambles are similarly ordered, or more generally positively quadrant dependent, then the risk index of the sum of two gambles is always larger than the minimum of the risk indices of the two gambles. For negative dependence, the risk index of the sum is always smaller than the maximum of the two risk indices. The above results agree with our intuitions well. For example, the result for negative dependence agrees with our intuition of risk diversification. Thus this result can be considered another attractive property of Aumann and Serrano's risk index.

Item Type: | MPRA Paper |
---|---|

Original Title: | Aumann and Serrano's Economic Index of Risk for Sums of Gambles |

English Title: | Aumann and Serrano's Economic Index of Risk for Sums of Gambles |

Language: | English |

Keywords: | Risk index; Additive gambles; Subadditivity; Positive quadrant dependence |

Subjects: | A - General Economics and Teaching > A1 - General Economics > A10 - General C - Mathematical and Quantitative Methods > C0 - General > C00 - General D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty |

Item ID: | 55697 |

Depositing User: | Minqiang Li |

Date Deposited: | 05 May 2014 14:27 |

Last Modified: | 05 Oct 2019 20:18 |

References: | Aumann, R.J., and R. Serrano, 2008. An economic index of riskiness. {\it Journal of Political Economy} 116(5), 810--836. Finner, H., 1992. A generalization of H\"{o}lder's inequality and some probability inequalities. {\it Annals of Probability} 20(4), 1893--1901. Hardy, G.H., J.E. Littlewood, and G. P\'{o}lya, 1934. {\it Inequalities}, Cambridge University Press. Kuptsov, L.P., 2001. {\it H\"{o}lder Inequality}, in Encyclopedia of Mathematics (edited by Hazewinkel M.), Kluwer Academic Publishers. Lehmann, E.L., 1966. Some concepts of dependence. {\it Annals of Mathematical Statistics} 37(5), 1137--1153. Merton R.C., 1990. {\it Continuous--time Finance}, Blackwell Publishing. Mitrinovi\'{c}, D.S., J. Pe\v{c}ari\'{c}, and A.M. Fink, 1992. {\it Classical and New Inequalities in Analysis (Mathematics and its Applications)}, Kluwer Academic Publishers. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/55697 |