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Approaches to conditional risk

Author

Listed:
  • Damir FILIPOVIC

    (Ecole Polytechnique Federale de Lausanne and Swiss Finance Institute)

  • Michael KUPPER

    (Humboldt Universität zu Berlin)

  • Nicolas VOGELPOTH

    (Morgan Stanleyl)

Abstract

We present and compare two di erent approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on Lp spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are de ned on Lp type modules. Both approaches utilize general duality theory for vector valued convex functions in contrast to the current literature in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures.

Suggested Citation

  • Damir FILIPOVIC & Michael KUPPER & Nicolas VOGELPOTH, 2011. "Approaches to conditional risk," Swiss Finance Institute Research Paper Series 11-02, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1102
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    File URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1752851
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    Citations

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    Cited by:

    1. Raimund M. Kovacevic & Georg Ch Pflug, 2014. "Are Time Consistent Valuations Information Monotone?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-33.
    2. Drapeau, Samuel & Jamneshan, Asgar, 2016. "Conditional preference orders and their numerical representations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 106-118.
    3. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    4. Samuel Drapeau & Asgar Jamneshan, 2014. "Conditional Preference Orders and their Numerical Representations," Papers 1410.5466, arXiv.org, revised Jan 2016.

    More about this item

    Keywords

    Conditional risk measures; L0-modules; Lp type modules; Monotone hulls; Subcash invariant hulls; Cash invariant hulls;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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