In risk models, the ruin probabilities and Lundberg bound are calculated despite knowing the statistical distribution of random
 variables. In the present paper, for collective risk model and discrete time risk model of insurance company for independent
 and identically distributed claims with light-tailed distribution, the infinite time ruin probabilities are computed using Lund
berg bound, moreover the general forms of density functions of random variables of claim sizes are derived. For some special
 cases in the discrete time risk model, the density functions of claim sizes have the shifted geometric distribution, and for the
 collective risk model, they always have an exponential distribution. Presenting the numerical examples of infinite time ruin
 probabilities and the simulated values of these probabilities and the Lundberg bound are the final results of this article.