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Aggregation of 1-year risks in life and disability insurance

  • Boualem Djehiche (a1) and Björn Löfdahl (a1)
Abstract

We consider large insurance portfolios consisting of life or disability insurance policies that are assumed independent, conditional on a stochastic process representing the economic–demographic environment. Using the conditional law of large numbers, we show that when the portfolio of liabilities becomes large enough, its value on a δ-year horizon can be approximated by a functional of the environment process. Based on this representation, we derive a semi-analytical approximation of the systematic risk quantiles of the future liability value for a homogeneous portfolio when the environment is represented by a one-factor diffusion process. For the multi-factor diffusion case, we propose two different risk aggregation techniques for a portfolio consisting of large, homogeneous pools. We give numerical results comparing the resulting capital charges with the Solvency II standard formula, based on disability claims data from the Swedish insurance company Folksam.

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Copyright
Corresponding author
*Correspondence to: Björn Löfdahl, Department of Mathematics, Matematisk Statistik, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden. E-mail: bjornlg@kth.se
References
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Aro, H., Djehiche, B. & Lofdahl, B. (2015). Stochastic modelling of disability insurance in a multi-period framework. Scandinavian Actuarial Journal, 2015(1), 88106.
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Djehiche, B. & Löfdahl, B. (2014 a). A hidden Markov approach to disability insurance. arXiv preprint arXiv:1412.7334.
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Annals of Actuarial Science
  • ISSN: 1748-4995
  • EISSN: 1748-5002
  • URL: /core/journals/annals-of-actuarial-science
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