Summary: The interest force accumulated process is modeled by a standard Brownian motion and a Poisson process. By a martingale approach, Lundberg’s fundamental equation is obtained and two efficient applications of its solutions are considered. Hence some results about the probability of ruin and the probability that the surplus reaches a given level

$x$ $(x>u)$ are obtained. The results are a generalization of

*H. U. Gerber* and

*E. S. W. Shiu* [Insur. Math. Econ. 24, 3–14 (1999;

Zbl 0939.91065)] under constant interest force. Finally, some results are obtained when the individual claim amount obeys the exponential distribution with parameter

$\alpha $.