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Impact of correlation crises in risk theory: Asymptotics of finite-time ruin probabilities for heavy-tailed claim amounts when some independence and stationarity assumptions are relaxed


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  • Biard, Romain
  • Lefèvre, Claude
  • Loisel, Stéphane


In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax the independence and stationarity assumptions and extend some asymptotic results on finite-time ruin probabilities, to take into account possible correlation crises like the one recently bred by the sub-prime crisis: claim amounts, in general assumed to be independent, may suddenly become strongly positively dependent. The impact of dependence and non-stationarity is analyzed and several concrete examples are given.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 43 (2008)
Issue (Month): 3 (December)
Pages: 412-421

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Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:412-421

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Keywords: Finite-time ruin probabilities Ruin theory Correlation crisis Sub-prime effect Processes with dependent increments Asymptotic behavior Non-stationarity Heavy-tailed claim size distribution;


References listed on IDEAS
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  1. Cossette, Helene & Marceau, Etienne, 2000. "The discrete-time risk model with correlated classes of business," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 26(2-3), pages 133-149, May.
  2. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 29(3), pages 375-386, December.
  3. Frostig, Esther, 2003. "Ordering ruin probabilities for dependent claim streams," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 32(1), pages 93-114, February.
  4. Alink, Stan & Lowe, Matthias & V. Wuthrich, Mario, 2004. "Diversification of aggregate dependent risks," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(1), pages 77-95, August.
  5. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  6. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 35(2), pages 245-254, October.
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Cited by:
  1. Laurent Devineau & Stéphane Loisel, 2009. "Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?," Post-Print, HAL hal-00403662, HAL.
  2. Romain Biard, 2013. "Asymptotic multivariate finite-time ruin probabilities with heavy-tailed claim amounts: Impact of dependence and optimal reserve allocation," Post-Print, HAL hal-00538571, HAL.
  3. Stéphane Loisel & Christian Mazza & Didier Rullière, 2009. "Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes," Post-Print, HAL hal-00168716, HAL.
  4. Stéphane Loisel & Xavier Milhaud, 2011. "From deterministic to stochastic surrender risk models: impact of correlation crises on economic capital," Post-Print, HAL hal-00502847, HAL.
  5. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 51(2), pages 457-461.


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