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Keywords:

Science & Technology, Social Sciences, Physical Sciences, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Statistics & Probability, Mathematics, Mathematical Methods In Social Sciences, mutual exclusivity, stop-loss transform, tail convex order, risk measures, STOP-LOSS PREMIUMS, RISK AGGREGATION, DEPENDENCE, VARIABLES, 0102 Applied Mathematics, 1502 Banking, Finance and Investment, 3502 Banking, finance and investment, 4901 Applied mathematics, 4905 Statistics

Abstract:

© 2015 Taylor & Francis. In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding Value-at-Risks (VaRs) is possible, the other components being zero in such a case. No condition is imposed when all components stay below the VaRs. Several properties of this new negative dependence concept are derived. We show that this dependence structure gives rise to the smallest value of Tail-VaR (TVaR) of a sum of risks within a given Fréchet space, provided that the probability level of the TVaR is close enough to one.