2014/01/15 by Boualem Djehiche, Djehiche, Boualem, Björn Löfdahl +1
Economics, Econometrics and Finance · #FOS: Economics and business #Risk Management (q-fin.RM) #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1401.3589
arxiv created 2014/08/26 · arxiv updated 2014/08/27
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.