We consider the dividends problem for both de Finetti's and Dual models for spectrally one-sided L\'evy processes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness condition in both models are satisfied, thus there is no duality gap. Therefore the optimal value function can be obtained as the point-wise infimum of auxiliary value functions indexed by Lagrange multipliers. We also present a numerical example.
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