Risk aggregation and stochastic claims reserving in disability insurance

Boualem Djehiche; Björn Löfdahl

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arXiv · 1401.3589

Risk aggregation and stochastic claims reserving in disability insurance

Boualem Djehiche·Björn Löfdahl

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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, Björn Löfdahl. 2014-08-26. Risk aggregation and stochastic claims reserving in disability insurance. https://arxiv.org/abs/1401.3589

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