Abstract
The fall of AIG is another confirmation that the insurance businessis not immune to bankruptcy. Contrary to the actuarial literaturewhich postulates that insurance firms can survive forever, we believethat this is not the case, and that a realistic and business-oriented riskmanagement approach needs to be designed in order to prevent the actual,finite-time, bankruptcy of insurance companies. In this article wemodel the surplus process of an insurance firm firstly by a stable L?evyprocess, secondly by a double exponential compound Poisson process.We compute finite-time survival and bankruptcy probabilities undersuch hypotheses. To achieve this, we make use of the Wiener-Hopffactorization and compute bankruptcy formulas written in terms of inverseLaplace transforms. The Abate and Whitt, and Gaver-Stehfestalgorithms are used to obtain numerical estimations.