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Stochastic orders and co-risk measures under positive dependence

M.A. Sordo, A.J. Bello and A. Suárez-Llorens

Insurance: Mathematics and Economics, 2018, vol. 78, issue C, 105-113

Abstract: Conditional risk measures (or co-risk measures) and risk contribution measures are increasingly used in actuarial portfolio analysis to evaluate the systemic risk, which is related to the risk that the failure or loss of a component spreads to another component or even to the whole portfolio: while co-risk measures are risk-adjusted versions of measures usually employed to assess isolate risks, risk contribution measures quantify how a stress situation for a component affects another one. In this paper, we provide sufficient conditions under which two random vectors could be compared in terms of CoVaR (conditional value-at-risk), CoES (conditional expected shortfall) and different risk contribution measures. Conditions are given in terms of the increasing convex order, the dispersive order and the excess wealth order of the marginals under some assumptions of positive dependence.

Keywords: Co-risk measures; Stochastic orderings; CoVaR; CoES; Risk contribution; Dispersive order; Increasing convex order; Excess wealth order (search for similar items in EconPapers)
JEL-codes: G22 (search for similar items in EconPapers)
Date: 2018
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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