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Risk aggregation and stochastic claims reserving in disability insurance

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  • Boualem Djehiche
  • Bjorn Lofdahl

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.

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  • Boualem Djehiche & Bjorn Lofdahl, 2014. "Risk aggregation and stochastic claims reserving in disability insurance," Papers 1401.3589, arXiv.org, revised Aug 2014.
    • Handle: RePEc:arx:papers:1401.3589
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