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

Risks. 2019. Vol. 7. No. 1. Article 13.

Junca M., Harold A. Moreno-Franco, Pérez J.

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.

Ключевые слова: Оптимальное управление, выплата дивидендов, Dividend payment, Optimal control, Scale functions, Capital injection constraint, Spectrally negative Lévy processes, Reflected Lévy processes, Ограничение вложения капитала, Спектрально негативные процессы Леви, Отраженные процессы Леви, Масштабные функции