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Convex risk measures: Basic facts, law-invariance and beyond, asymptotics for large portfolios

In: HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II

Author

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  • Hans Föllmer
  • Thomas Knispel

Abstract

This paper provides an introduction to the theory of capital requirements defined by convex risk measures. The emphasis is on robust representations, law-invariant convex risk measures and their robustification in the face of model uncertainty, asymptotics for large portfolios, and on the connections of convex risk measures to actuarial premium principles and robust preferences.

Suggested Citation

  • Hans Föllmer & Thomas Knispel, 2013. "Convex risk measures: Basic facts, law-invariance and beyond, asymptotics for large portfolios," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part II, chapter 30, pages 507-554, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814417358_0030
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    Citations

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    Cited by:

    1. Pitera, Marcin & Schmidt, Thorsten, 2018. "Unbiased estimation of risk," Journal of Banking & Finance, Elsevier, vol. 91(C), pages 133-145.
    2. Marcin Pitera & Thorsten Schmidt, 2016. "Unbiased estimation of risk," Papers 1603.02615, arXiv.org, revised Aug 2017.
    3. Martin Herdegen & Nazem Khan, 2022. "Mean‐ρ$\rho$ portfolio selection and ρ$\rho$‐arbitrage for coherent risk measures," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 226-272, January.
    4. Hans Buehler & Phillip Murray & Mikko S. Pakkanen & Ben Wood, 2021. "Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics," Papers 2103.11948, arXiv.org, revised Jul 2021.
    5. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2018. "Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity," European Journal of Operational Research, Elsevier, vol. 264(2), pages 707-716.
    6. Marcelo Brutti Righi, 2018. "A theory for combinations of risk measures," Papers 1807.01977, arXiv.org, revised May 2023.
    7. Föllmer Hans, 2014. "Spatial risk measures and their local specification: The locally law-invariant case," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 79-101, March.
    8. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.
    9. Hans Rau-Bredow, 2019. "Bigger Is Not Always Safer: A Critical Analysis of the Subadditivity Assumption for Coherent Risk Measures," Risks, MDPI, vol. 7(3), pages 1-18, August.

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