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Star-shaped Risk Measures

Erio Castagnoli, Giacomo Cattelan, Fabio Maccheroni, Claudio Tebaldi and Ruodu Wang

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Abstract: In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity property of coherent risk measures is dispensed with and positive homogeneity is weakened, include all practically used risk measures, in particular, both convex risk measures and Value-at-Risk. From a financial viewpoint, our relaxation of convexity is necessary to quantify the capital requirements for risk exposure in the presence of competitive delegation or robust aggregation mechanisms. From a decision theoretical perspective, star-shaped risk measures emerge from variational preferences when risk mitigation strategies can be adopted by a rational decision maker.

Date: 2021-03
New Economics Papers: this item is included in nep-rmg
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