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Open AccessArticle

Optimal Bail-Out Dividend Problem with Transaction Cost and Capital Injection Constraint

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Department of Mathematics, Universidad de los Andes, Bogotá 11711, Colombia
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Department of Mathematics and Statistics, Universidad del Norte, Barranquilla 080003, Colombia
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Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C., Guanajuato 36000, Mexico
*
Author to whom correspondence should be addressed.
Risks 2019, 7(1), 13; https://doi.org/10.3390/risks7010013
Received: 18 December 2018 / Revised: 28 January 2019 / Accepted: 29 January 2019 / Published: 31 January 2019
We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and capital injection and show the optimality of reflected ( c 1 , c 2 ) -policies. We then find the optimal Lagrange multiplier, by showing that in the dual Lagrangian problem the complementary slackness conditions are met. Finally, we present some numerical examples to support our results. View Full-Text
Keywords: dividend payment; optimal control; capital injection constraint; spectrally negative Lévy processes; reflected Lévy processes; scale functions dividend payment; optimal control; capital injection constraint; spectrally negative Lévy processes; reflected Lévy processes; scale functions
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Junca, M.; Moreno-Franco, H.A.; Pérez, J.L. Optimal Bail-Out Dividend Problem with Transaction Cost and Capital Injection Constraint. Risks 2019, 7, 13.

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