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Star-Shaped Risk Measures

Author

Listed:
  • Erio Castagnoli

    (Department of Decision Sciences, Bocconi University, Milan 20100, Italy)

  • Giacomo Cattelan

    (Department of Economics, New York University, New York, New York 10012)

  • Fabio Maccheroni

    (Department of Decision Sciences, Bocconi University, Milan 20100, Italy)

  • Claudio Tebaldi

    (Department of Finance, Bocconi University, Milan 20100, Italy)

  • Ruodu Wang

    (Department of Statistics and Actuarial Science, University of Waterloo, Ontario N2L3G1, Canada)

Abstract

In this paper, monetary risk measures that are positively superhomogeneous, called star-shaped risk measures , are characterized and their properties are studied. The measures in this class, which arise when the 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.

Suggested Citation

  • Erio Castagnoli & Giacomo Cattelan & Fabio Maccheroni & Claudio Tebaldi & Ruodu Wang, 2022. "Star-Shaped Risk Measures," Operations Research, INFORMS, vol. 70(5), pages 2637-2654, September.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:5:p:2637-2654
    DOI: 10.1287/opre.2022.2303
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