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Intrinsic risk measures

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  • W. Farkas
  • A. Smirnow

Abstract

Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach provides a direct path from unacceptable positions towards the acceptance set. Intrinsic risk measures use only internal resources and return the smallest percentage of the currently held financial position which has to be sold and reinvested into an eligible asset such that the resulting position becomes acceptable. While avoiding the problem of infinite values, intrinsic risk measures allow a free choice of the eligible asset and they preserve desired properties such as monotonicity and quasi-convexity. A dual representation on convex acceptance sets is derived and the link of intrinsic risk measures to their monetary counterparts on cones is detailed.

Suggested Citation

  • W. Farkas & A. Smirnow, 2016. "Intrinsic risk measures," Papers 1610.08782, arXiv.org.
    • Handle: RePEc:arx:papers:1610.08782
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    References listed on IDEAS

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    1. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Capital requirements with defaultable securities," Papers 1203.4610, arXiv.org, revised Jan 2014.
    2. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    3. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    4. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Risk Measures: Rationality and Diversification," Carlo Alberto Notebooks 100, Collegio Carlo Alberto.
    5. Artzner, Philippe & Delbaen, Freddy & Koch-Medina, Pablo, 2009. "Risk Measures and Efficient use of Capital 1," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 101-116, May.
    6. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. Konstantinides, Dimitrios G. & Kountzakis, Christos E., 2011. "Risk measures in ordered normed linear spaces with non-empty cone-interior," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 111-122, January.
    9. Samuel Drapeau & Michael Kupper, 2013. "Risk Preferences and Their Robust Representation," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 28-62, February.
    10. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Beyond cash-additive risk measures: when changing the num\'{e}raire fails," Papers 1206.0478, arXiv.org, revised Feb 2014.
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