Abstract

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.