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

Author

Listed:
  • Mauricio Junca

    (Department of Mathematics, Universidad de los Andes, Bogotá 11711, Colombia)

  • Harold A. Moreno-Franco

    (Department of Mathematics and Statistics, Universidad del Norte, Barranquilla 080003, Colombia)

  • José Luis Pérez

    (Department of Probability and Statistics, Centro de Investigación en Matemáticas A.C., Guanajuato 36000, Mexico)

Abstract

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.

Suggested Citation

  • Mauricio Junca & Harold A. Moreno-Franco & José Luis Pérez, 2019. "Optimal Bail-Out Dividend Problem with Transaction Cost and Capital Injection Constraint," Risks, MDPI, vol. 7(1), pages 1-24, January.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:13-:d:202392
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2014. "Optimal dividends in the dual model under transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 133-143.
    2. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    3. Hernández, Camilo & Junca, Mauricio & Moreno-Franco, Harold, 2018. "A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 57-68.
    4. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    5. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 359-372, September.
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    Cited by:

    1. Wenyuan Wang & Yuebao Wang & Ping Chen & Xueyuan Wu, 2022. "Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 924-965, September.
    2. Florin Avram & Dan Goreac & Juan Li & Xiaochi Wu, 2021. "Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model," Mathematics, MDPI, vol. 9(9), pages 1-27, April.

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