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This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the no-reinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations. • We provide a validation of the Dual Linear Programming algorithm by showcasing its performance on two benchmarks. • With a relatively modest order of moments (4), the relative errors are of at most 3%. • Leveraging this algorithm reveals significant enhancements in the expected dividends, advocating for capital injections. [ABSTRACT FROM AUTHOR]