Extended Gini-type measures of risk and variability

Berkhouch, Mohammed and Lakhnati, Ghizlane (2017): Extended Gini-type measures of risk and variability.

Abstract

The main of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior. Our risk measures family is coherent and catches variability with respect to the decision-maker attitude towards risk.

• Item Type: MPRA Paper
• Language: English
• Keywords: risk measure, variability measure, risk aversion, signed Choquet integral, Extended Gini Shortfall
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; G - Financial Economics > G1 - General Financial Markets > G10 - General

References

Acerbi, C. (2002). Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26, 1505-1518.

Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203-228.

Ceriani, L. and Verme, P. (2012) The origins of the Gini index: extracts from Variabilit`a e Mutabilit`a (1912) by Corrado Gini. Journal of Economic Inequality, 10, 421-443.

Choquet, G. (1954). Theory of capacities. Annales de linstitut Fourier, 5, 131-295.

Dana, R.-A. (2005). A representation result for concave Schur-concave functions. Mathematical Finance, 15, 613-634.

Delbaen, F. (2012): Monetary Utility Functions. Osaka University Press, Osaka.

Embrechts, P., Puccetti, G., R¨uschendorf, L., Wang, R. and Beleraj, A. (2014). An academic response to Basel 3.5. Risks, 2, 25-48.

F¨ollmer, H. and Schied, A. (2011). Stochastic Finance: An Introduction in Discrete Time. (Third Edition.) Walter de Gruyter, Berlin.

Furman, E. and Landsman, Z. (2006a). Tail variance premium with applications for elliptical portfolio of risks. ASTIN Bulletin: Journal of the International Actuarial Association, 36, 433-462.

Furman, E., Wang, R. and Zitikis, R. (2017). Gini-type measures of risk and variability: Gini shortfall, capital allocation and heavy-tailed risks. Journal of Banking and Finance, minor revision.

Giorgi, G.M. (1990) Bibliographic portrait of the Gini concentration ratio. Metron, 48, 183-221.

Giorgi, G.M. (1993) A fresh look at the topical interest of the Gini concentration ratio. Metron, 51, 83-98.

Grechuk, B., Molyboha, A. and Zabarankin, M. (2009). Maximum entropy principle with general deviation measures. Mathematics of Operations Research, 34, 445-467.

Mao, T. and Wang, R. (2016). Risk aversion in regulatory capital principles.

McNeil, A.J., Frey, R. and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools. (Revised Edition.) Princeton University Press, Princeton, NJ.

Rockafellar, R. T., Uryasev, S. and Zabarankin, M. (2006). Generalized deviation in risk analysis. Finance and Stochastics, 10, 51-74.

R¨uschendorf, L. (2013). Mathematical Risk Analysis. Dependence, Risk Bounds, Optimal Allocations and Portfolios. Springer, Heidelberg.

Schmeidler, D. (1986). Integral representation without additivity. Proceedings of the American Mathematical Society, 97, 255-261.

Schmeidler, D. (1989). Subject probability and expected utility without additivity. Econometrica, 57(3), 571-587.

Shalit, H., and Yitzhaki, S. (1984). Mean-Gini, portfolio theory and the pricing of risky assets. Journal of Finance, 39(5 (December)), 1449-1468.

Wang, R., Wei, Y. and Willmot., G.E. (2017). Characterization, Robustness and Aggregation of Signed Choquet Integrals. Working paper.

Yaari, M.E. (1987). The dual theory of choice under risk. Econometrica, 55, 95-115.

Yitzhaki, S. (1983) On an extension of Gini inequality index, International Economic Review, 24, no. 3, 617-628.

Yitzhaki, S. (1998) More than a dozen alternative ways of spelling Gini, Research on Economic Inequality, 8, 13-30.

Yitzhaki, S. and Schechtman, E. (2005). The properties of the extended Gini measures of variability and inequality. Metron, LXIII(3), 401-443.

Yitzhaki, S. and Schechtman, E. (2013). The Gini Methodology: A Primer on a Statistical Methodology. Springer, New York, NY.