In this talk, I will present some recent results on the finite-time ruin problems for the classical risk model and that perturbed by diffusion. Specifically, we study the finite-time expected discounted penalty function (EDPF). Using some techniques developed recently, we show that the finite-time EDPFs can be expressed in terms of their corresponding ones under the infinite-time horizon. In the perturbed risk model case, we find that the finite-time ruin probability due to oscillations and the finite-time ruin probability caused by a claim can also be expressed in terms of the corresponding quantities under the infinite-time horizon. Numerical examples are given when claims follow an exponential distribution.