Analytic properties of infinite-horizon survival probability in a risk model with additional funds (Q2786953)

A classical risk model is considered where at claim times additional income is added to the surplus. It is first shown that the model can be seen as a risk model with two-sided jumps. A net profit condition is assumed. It is then shown that the ruin probability is absolutely continuous and differentiable at the points of continuity of the distribution function of the downward jumps. In the case where the jumps on both sides are exponentially distributed, the ruin probability can be calculated explicitly. A similar model, without the continuous premium income, is considered in [\textit{A. V. Boikov}, Probab. Appl. 47, No. 3, 489--493 (2002; Zbl 1033.60093)].