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Dividends: From Refracting to Ratcheting

Author

Listed:
  • Hansjoerg Albrecher

    (University of Lausanne and Swiss Finance Institute)

  • Nicole Bäuerle

    (University of Karlsruhe)

  • Martin Bladt

    (University of Lausanne)

Abstract

In this paper we consider an alternative dividend payment strategy in risk theory, where the dividend rate can never decrease. This addresses a concern that has often been raised in connection with the practical relevance of optimal classical dividend payment strategies of barrier and threshold type. We study the case where once during the lifetime of the risk process the dividend rate can be increased and derive corresponding formulae for the resulting expected discounted dividend payments until ruin. We first consider a general spectrally-negative Lévy risk model, and then re fine the analysis for a diffusion approximation and a compound Poisson risk model. It is shown that for the diffusion approximation the optimal barrier for the ratcheting strategy is characterized by an unexpected relation to the case of refracted dividend payments. Finally, numerical illustrations for the diffusion case indicate that with such a simple ratcheting dividend strategy the expected value of discounted dividends can already get quite close to the respective value of the refracted dividend strategy, the latter being known to be optimal among all admissible dividend strategies.

Suggested Citation

  • Hansjoerg Albrecher & Nicole Bäuerle & Martin Bladt, 2018. "Dividends: From Refracting to Ratcheting," Swiss Finance Institute Research Paper Series 18-32, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1832
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3169185
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    Citations

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    Cited by:

    1. Hansjörg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividends under a drawdown constraint and a curious square-root rule," Finance and Stochastics, Springer, vol. 27(2), pages 341-400, April.
    2. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2022. "Optimal dividends under a drawdown constraint and a curious square-root rule," Papers 2206.12220, arXiv.org.
    3. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    4. Chonghu Guan & Zuo Quan Xu, 2023. "Optimal ratcheting of dividend payout under Brownian motion surplus," Papers 2308.15048, arXiv.org, revised Jul 2024.
    5. Tim J. Boonen & Engel John C. Dela Vega, 2024. "Optimal Ratcheting of Dividends with Irreversible Reinsurance," Papers 2408.16989, arXiv.org.
    6. Piotr Jaworski & Kamil Liberadzki & Marcin Liberadzki, 2021. "On Write-Down/ Write-Up Loss Absorbing Instruments," European Research Studies Journal, European Research Studies Journal, vol. 0(1), pages 1204-1219.
    7. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2019. "Optimal ratcheting of dividends in insurance," Papers 1910.06910, arXiv.org, revised Jun 2021.

    More about this item

    Keywords

    optimal dividends; risk theory; Levy risk model; scale functions; diffusion;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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