2021/03/29 by Erio Castagnoli, Giacomo Cattelan, Castagnoli, Erio +7 · 4 citations
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Functional Analysis (math.FA) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Stochastic processes and financial applications #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2103.15790
openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 liquidity risk, 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.