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

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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 DecisionMaking 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), 810836. Finner, H., 1992. A generalization of H\"{o}lder's inequality and some probability inequalities. {\it Annals of Probability} 20(4), 18931901. 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), 11371153. Merton R.C., 1990. {\it Continuoustime 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.unimuenchen.de/id/eprint/55697 