  In this paper, we introduce a new model for the risk process based on general
compound Hawkes process (GCHP) for the arrival of claims. We call it risk model
based on general compound Hawkes process (RMGCHP). The Law of Large Numbers
(LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study
the main properties of this new risk model, net profit condition, premium
principle and ruin time (including ultimate ruin time) applying the LLN and
FCLT for the RMGCHP. We show, as applications of our results, similar results
for risk model based on compound Hawkes process (RMCHP) and apply them to the
classical risk model based on compound Poisson process (RMCPP).
