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Properties of a risk measure derived from the expected area in red


Author Info

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Julien Trufin

    (Ecole d'Actuariat - Université Laval)


This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a fixed time interval [0; T] (T can be infinite) is less than a given predetermined risk limit. We also investigate the optimal risk limit allocation: given a risk limit set at company level for the sum of the expected areas in red of all lines, we determine the way(s) to allocate this risk limit to the subsequent business lines in order to minimize the overall capital needs.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00870224.

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Date of creation: 04 Oct 2013
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Handle: RePEc:hal:wpaper:hal-00870224

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Keywords: Ruin probability; risk measure; expected area in red; stochastic ordering; risk limit;

This paper has been announced in the following NEP Reports:


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  1. Picard, Philippe, 1994. "On some measures of the severity of ruin in the classical Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 107-115, May.
  2. Stéphane Loisel, 2005. "Differentiation of some functionals of risk processes," Post-Print hal-00157739, HAL.
  3. Romain Biard & Stéphane Loisel & Claudio Macci & Noel Veraverbeke, 2010. "Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation," Post-Print hal-00372525, HAL.
  4. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
  5. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2006. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 10(3), pages 427-448, September.
  6. Gerber, Hans U., 1988. "Mathematical fun with ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 15-23, January.
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