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.
We evaluate the probability of bivariate ruin in finite time by using logistical copulas and by considering the laws of claims and of by-claims, respectively, modeled by an α-stable distribution and a β-stable distribution.

stable distribution Brownian perturbation by-claim heavy tail distribution renewal equation