Risk aggregation and stochastic claims reserving in disability insurance
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.
Keywords
Cite
@article{arxiv.1401.3589,
title = {Risk aggregation and stochastic claims reserving in disability insurance},
author = {Boualem Djehiche and Björn Löfdahl},
journal= {arXiv preprint arXiv:1401.3589},
year = {2014}
}