In a Brownian risk model with capital injections and ruin penalty, optimal absolutely continuous dividend strategies with affine rate bound exhibit a Løkka-Zervos dichotomy: either bail-outs prevent ruin or no injections occur and bankruptcy is possible, with full-rate dividends above a threshold.
Jeanblanc-Picqué and A
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A simple approach to the L{\o}kka-Zervos dichotomy for absolutely continuous dividend strategies
In a Brownian risk model with capital injections and ruin penalty, optimal absolutely continuous dividend strategies with affine rate bound exhibit a Løkka-Zervos dichotomy: either bail-outs prevent ruin or no injections occur and bankruptcy is possible, with full-rate dividends above a threshold.