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A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processes

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  • Hernández, Camilo
  • Junca, Mauricio
  • Moreno-Franco, Harold

Abstract

We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We consider De Finetti’s problem for one-sided Lévy risk models in both scenarios with and without fix transaction costs. To characterize the solution to the aforementioned models we introduce the dual problem and show that the complementary slackness conditions are satisfied and therefore there is no duality gap. As a consequence the optimal value function can be obtained as the pointwise infimum of auxiliary value functions. Finally, we illustrate our findings with a series of numerical examples.

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  • 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.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:57-68
    DOI: 10.1016/j.insmatheco.2017.12.011
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    References listed on IDEAS

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    Cited by:

    1. Yangmin Zhong & Huaping Huang, 2023. "Cash Flow Optimization on Insurance: An Application of Fixed-Point Theory," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    2. Christian Hipp, 2018. "Company Value with Ruin Constraint in Lundberg Models," Risks, MDPI, vol. 6(3), pages 1-15, July.
    3. 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.
    4. Xu, Ran & Woo, Jae-Kyung, 2020. "Optimal dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 1-16.
    5. Soren Christensen & Kristoffer Lindensjo, 2019. "Moment constrained optimal dividends: precommitment \& consistent planning," Papers 1909.10749, arXiv.org.
    6. 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.

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