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From deterministic to stochastic surrender risk models: impact of correlation crises on economic capital

  • Stéphane Loisel

    ()

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

  • Xavier Milhaud

    ()

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

In this paper we raise the matter of considering a stochastic modeling of the surrender rate instead of the classical S-shaped deterministic curve (in function of the spread), still used in almost all insurance companies. A stochastic model in which surrenders are conditionally independent with respect to a S-curve disturbance would be tempting in some extreme scenarii, especially to address the question of the lack of data. However, we explain why this conditional independence between policyholders, which has the advantage to be the simplest assumption, looks particularly maladaptive when the spread increases. Indeed the correlation between policyholders' decisions is most likely to increase in this situation. We suggest and develop a simple model which integrates those phenomena. With stochastic orders it is possible to compare it to the conditional independence approach qualitatively. In an partially internal Solvency II model, we quantify the impact of the correlation phenomenon on a real life portfolio for a global risk management strategy.

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Paper provided by HAL in its series Post-Print with number hal-00502847.

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Date of creation: 2011
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Publication status: Published, European Journal of Operational Research, 2011, 214, 2, 348-357
Handle: RePEc:hal:journl:hal-00502847
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00502847
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  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-00403662, HAL.
  2. Xavier Milhaud & Marie-Pierre Gonon & Stéphane Loisel, 2010. "Les comportements de rachat en Assurance Vie en régime de croisière et en période de crise," Post-Print hal-00502851, HAL.
  3. Biard, Romain & Lefèvre, Claude & Loisel, Stéphane, 2008. "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," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 412-421, December.
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