RISK MEASURES: RATIONALITY AND DIVERSIFICATION |
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Authors: | Simone Cerreia‐Vioglio Fabio Maccheroni Massimo Marinacci Luigi Montrucchio |
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Affiliation: | 1. Department of Decision Sciences and IGIER, Università Bocconi;2. Department of Decision Sciences, Dondena, and IGIER, Università Bocconi;3. Collegio Carlo Alberto, Università di Torino |
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Abstract: | When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash‐additivity assumption on risk measures becomes problematic. When this assumption is weakened, to cash‐subadditivity for example, the equivalence between convexity and the diversification principle no longer holds. In fact, this principle only implies (and it is implied by) quasiconvexity. For this reason, in this paper quasiconvex risk measures are studied. We provide a dual characterization of quasiconvex cash‐subadditive risk measures and we establish necessary and sufficient conditions for their law invariance. As a byproduct, we obtain an alternative characterization of the actuarial mean value premium principle. |
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Keywords: | risk measures diversification cash‐subadditivity quasiconvexity law‐invariance mean value premium principle |
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