<p>This paper investigates the optimal management of a firm’s financial resources by formulating a joint capital injection and dividend optimization problem in which the surplus process evolves as a general integrable Lévy process accommodating both positive and negative jumps. I characterize the value function of the control problem as the unique viscosity solution to a Hamilton-Jacobi-Bellman variational inequality, under semi-state constraints. A key result reveals a dichotomy in optimal capital injection strategies: either it is optimal to inject capital only when the surplus becomes negative up to a specific threshold, or it is never optimal to inject at all. The nature of the negative jumps – finite versus infinite variation – affects the boundary conditions and the structure of the optimal strategy. In the second part, assuming finite activity of negative jumps, I provide a complete characterization of the optimal dividend strategy, identifying a threshold above which immediate dividend payments are optimal.</p>