On the Bankruptcy Risk of Insurance Companies

The fall of AIG proved that the insurance business is not immune to bankruptcy, contrary to the actuarial literature which postulates that insurance firms can survive forever. 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. This article can be viewed as an illustration of a general approach to the bankruptcy of financial institutions.