On Partial Stochastic Comparisons Based on Tail Values at Risk

Alfonso J. Bello, Julio Mulero, Miguel A. Sordo and Alfonso Suárez-Llorens
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Alfonso J. Bello: Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain
Julio Mulero: Dpto. Matemáticas, Universidad de Alicante, Ap. 99, E-03080 Alicante, Spain
Miguel A. Sordo: Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain
Alfonso Suárez-Llorens: Dpto. Estadística e Investigación Operativa, Universidad de Cádiz, 11510 Puerto Real, Spain

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: The tail value at risk at level p , with p ∈ ( 0 , 1 ) , is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be used to decide which is riskier. When the tail values at risk of both distributions agree, whenever the probability level p ∈ ( 0 , 1 ) , about which of them is riskier, then the distributions are ordered in terms of the increasing convex order. The price to pay for such a unanimous agreement is that it is possible that two distributions cannot be compared despite our intuition that one is less risky than the other. In this paper, we introduce a family of stochastic orders, indexed by confidence levels p 0 ∈ ( 0 , 1 ) , that require agreement of tail values at risk only for levels p > p 0 . We study its main properties and compare it with other families of stochastic orders that have been proposed in the literature to compare tail risks. We illustrate the results with a real data example.

Keywords: value at risk; tail value at risk; stochastic orders; financial risk (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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