Usabel Rodrigo, Miguel Arturo2011-12-122011-12-121999-11Insurance, Mathematics & Economics, Nov. 1999, v. 25, n. 2, pp. 133-1420167-6687https://hdl.handle.net/10016/12733Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver–Stehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literatureapplication/pdfeng©ElsevierMultivariate ultimate ruin probabilityLaplace transformIntegral equationsNumerical methodsresearch articleG22IM13IM20Empresa10.1016/S0167-6687(99)00029-3open access1332142Insurance, Mathematics & Economics25