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Risk aggregation and stochastic claims reserving in disability insurance

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  • Djehiche, Boualem
  • Löfdahl, Björn

Abstract

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic–demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations.

Suggested Citation

  • Djehiche, Boualem & Löfdahl, Björn, 2014. "Risk aggregation and stochastic claims reserving in disability insurance," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 100-108.
    • Handle: RePEc:eee:insuma:v:59:y:2014:i:c:p:100-108
    DOI: 10.1016/j.insmatheco.2014.09.001
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