  This paper proposes a flexible and analytically tractable class of frequency
and severity models for predicting insurance claims. The proposed model is able
to capture nonlinear relationships in explanatory variables by characterizing
the logarithmic mean functions of frequency and severity distributions as
neural networks. Moreover, a potential dependence between the claim frequency
and severity can be incorporated. In particular, the paper provides analytic
formulas for mean and variance of the total claim cost, making our model ideal
for many applications such as pricing insurance contracts and the pure premium.
A simulation study demonstrates that our method successfully recovers nonlinear
features of explanatory variables as well as the dependency between frequency
and severity. Then, this paper uses a French auto insurance claim dataset to
illustrate that the proposed model is superior to the existing methods in
fitting and predicting the claim frequency, severity, and the total claim loss.
Numerical results indicate that the proposed model helps in maintaining the
competitiveness of an insurer by accurately predicting insurance claims and
avoiding adverse selection.
