Traditional claims reserve approaches are all based on aggregated
data and usually produce inaccurate projections of the reserve because the aggregated data
make a great loss of information contained in individual claims. Thus, the researcher in
actuarial science developed the so-called individual claim models that are based on marked
Poisson processes. However, due to the inappropriateness of Poisson distribution in
modelling the claims distributions, the present paper propose marked Cox processes as
reserve models. Compared with the aggregate claims models, the models proposed in the
current paper take more sufficient use of information contained in data and can be expected
to produce more accurate evaluations in claim loss reserving.