For Lévy risk processes with two-sided jumps, the optimal dividend and capital injection strategy is a double barrier rule: pay out the excess above a threshold and inject capital to prevent ruin.
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On the optimality of double barrier strategies for L\'evy processes
For Lévy risk processes with two-sided jumps, the optimal dividend and capital injection strategy is a double barrier rule: pay out the excess above a threshold and inject capital to prevent ruin.