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**Optimal barriers in a modified surplus process**

We obtain the optimal pair of initial surplus and barrier level in a lower barrier model of a modified surplus process. In particular, we examine the defective distribution function of the time to ruin with given lower barrier and initial surplus which is suggested by Nie et al. [Minimizing the ruin probability through capital injections. Ann Actuar Sci. 2011;5(2):195–209]. We aim to take this approach one step further by proposing optimal reinsurance under the minimum finite time ruin probability and maximum benefit criteria such as the released capital, expected profit and expected utility. We calculate the optimal pairs of initial surplus and barrier levels for different time periods, loading factors and weights of the criteria. We analyse the robustness of the results by a sensitivity analysis.

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