Stochastic loss reserving using individual information model with over-dispersed Poisson

For stochastic loss reserving, we propose an individual information model (IIM) which accommodates not only individual/micro data consisting of incurring times, reporting developments, settlement developments as well as payments of individual claims but also heterogeneity among policies. We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims. Model estimation is conducted under quasi-likelihood theory. Analytic expressions are derived for the expectation and variance of outstanding liabilities, given historical observations. We utilise conditional mean square error of prediction (MSEP) to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough, IIM shows a higher prediction accuracy than individual/micro data model (IDM) in predicting the outstanding liabilities, if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM. Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM. A real data analysis is performed basing on real observations in health insurance.