  We propose an asymptotic theory for distribution forecasting from the log
normal chain-ladder model. The theory overcomes the difficulty of convoluting
log normal variables and takes estimation error into account. The results
differ from that of the over-dispersed Poisson model and from the chain-ladder
based bootstrap. We embed the log normal chain-ladder model in a class of
infinitely divisible distributions called the generalized log normal
chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where
the dimension of the reserving triangle is kept fixed while the standard
deviation is assumed to decrease. The resulting asymptotic forecast
distributions follow t distributions. The theory is supported by simulations
and an empirical application.
