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Optimal dividend payment under time of ruin contraint: Exponential case

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  • Camilo Hernandez
  • Mauricio Junca

Abstract

We consider the classical optimal dividends problem under the Cram\'er-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions 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 series of numerical examples.

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  • Camilo Hernandez & Mauricio Junca, 2014. "Optimal dividend payment under time of ruin contraint: Exponential case," Papers 1410.3793, arXiv.org, revised May 2015.
    • Handle: RePEc:arx:papers:1410.3793
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    References listed on IDEAS

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    1. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
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    Cited by:

    1. Claudia Kluppelberg & Miriam Isabel Seifert, 2016. "Conditional loss probabilities for systems of economic agents sharing light-tailed claims with analysis of portfolio diversification benefits," Papers 1612.07132, arXiv.org.
    2. Camilo Hernandez & Mauricio Junca & Harold Moreno-Franco, 2016. "A time of ruin constrained optimal dividend problem for spectrally one-sided L\'evy processes," Papers 1608.02550, arXiv.org, revised May 2017.
    3. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.

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