The fall of AIG is another confirmation that the insurance business is not immune to bankruptcy. Contrary to the actuarial literature which postulates that insurance firms can survive forever, we believe that this is not the case, and that a realistic and business- oriented risk management approach needs to be designed in order to prevent the actual, finite-time, bankruptcy of insurance companies. In this article we model the surplus process of an insurance firm firstly by a stable Lévy process, secondly by a double exponential compound Poisson process. We compute finite-time survival and bankruptcy probabilities under such hypotheses. To achieve this, we make use of the Wiener-Hopf factorization and compute bankruptcy formulas written in terms of inverse Laplace transforms. The Abate and Whitt, and Gaver-Stehfest algorithms are used to obtain numerical estimations.