This paper contributes to the approach of the bivariate risk of ruin in finite time. We deal with a problem of risk of occurrence of a claim from the Cramer-Lundberg model in which there is some by-claim (more or less zero) integrating a Brownian oscillation at the level of the reserve at a given time t.

stable distribution, Brownian perturbation, by-claim, heavy tail distribution, renewal equation, copulas, classical risk model of ruin