Sometimes when there are some restrictions on the random variables of
insurance risk model, it is impossible to calculate the exact value of
ruin probabilities. For these cases, even finding a suitable
approximation, is very important from a practical point of view. In the
present paper, we consider the classical insurance surplus model with
light tailed claim amount distributions and try to find some
inequalities and optimal estimation on the infinite time ruin
probability depending on the amount of initial reserve when the
assumption of net profit does not hold but there exist some other
restrictions on the mathematical functions of random variables of model.
The obtained assertions depend on the amount of initial reserve,
distribution of nonnegative claim amounts and claim inter-arrival times.
Finally, to show the application and effectiveness of results some
examples are presented.