Li, Minqiang
(2013):
*On Aumann and Serrano's Economic Index of Risk.*

Preview |
PDF
MPRA_paper_47466.pdf Download (460kB) | Preview |

## Abstract

We study the risk index of an additive gamble proposed in Aumann and Serrano (2008).We establish a generalized duality result for this index and use it to prove Yaari's (1969) alternative characterization of DARA utilities. A new characterization result for the risk index is obtained through essentially monotonic risk aversion utilities. We also extend the domain of gambles by introducing a price for gambles. We then develop a theory on the risk index for multiplicative gambles. Relative risk aversion functions for multiplicative gambles play the same role as absolute risk aversion functions for additive gambles.

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

Original Title: | On Aumann and Serrano's Economic Index of Risk |

Language: | English |

Keywords: | Risk index Attractiveness index Duality Additive gambles Multiplicative gambles |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C00 - General D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty |

Item ID: | 47466 |

Depositing User: | Minqiang Li |

Date Deposited: | 10 Jun 2013 14:37 |

Last Modified: | 26 Sep 2019 13:40 |

References: | Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath, Coherent measures of risk, Mathe- matical Finance , 9, 203{228 (1999). Aumann, R.J., and R. Serrano, An economic index of riskiness, Journal of Political Economy, 116(5), 810{836 (2008). Chateauneuf, A., Cohen, M., Meilijson, I., More Pessimism than Greediness: A Characterization of Monotone Risk Aversion in the Rank-Dependent Expected Utility Model, Economic Theory, 25, 649{667 (2005). Chen, Y-C., X. Luo, An indistinguishability result on rationalizability under general preferences, Economic Theory, 51(1), 1{12 (2012). Cox, J.C., V. Sadiraj, B. Vogt, U. Dasgupta, Is there a plausible theory for decision under risk? A dual calibration critique, it Economic Theory, forthcoming (2013), DOI 10.1007/s00199-012-0712-4. Dybvig, P.H., and S.A. Lippman, An alternative characterization of decreasing absolute risk aversion, Econometrica, 51, 223{224 (1983). Eguia, J.X., On the spatial representation of preference pro¯les, Economic Theory, 52(1), 103{128 (2013) Finner, H., A generalization of HÄolder's inequality and some probability inequalities, Annals of Probability, 20(4), 1893{1901 (1992). Hardy, G.H., J.E. Littlewood, and G. P¶olya, Inequalities, Cambridge University Press (1934). Kuptsov, L.P., HÄolder Inequality, in Encyclopedia of Mathematics (edited by Hazewinkel M.), Kluwer Academic Publishers (2001). Lehmann, E.L., Some concepts of dependence, Annals of Mathematical Statistics, 37(5), 1137{1153 (1966). Markowitz, H., Portfolio selection, Journal of Finance, 7, 77{91 (1952). Merton R.C., Continuous{time Finance, Blackwell Publishing (1990). Mitrinovi¶c, D.S., J. Pe·cari¶c, and A.M. Fink, Classical and New Inequalities in Analysis (Mathematics and its Applications), Kluwer Academic Publishers (1992). Nielsen, L.T., Monotone risk aversion, Economic Theory, 25(1), 203{215 (2005). Pearson, N.D., Risk Budgeting: Portfolio Problem Solving with Value-at-Risk. John Wiley & Sons (2002). Pratt, J.W., Risk aversion in the small and in the large, Econometrica, 32, 122{136 (1964). Sharpe, W.F., Mutual fund performance, Journal of Business, 39, 119{138 (1966). Yaari, M.E., Some remarks on measures of risk aversion and on their uses, Journal of Economic Theory, 1, 315{329 (1969). |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/47466 |