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Optimal dividends under a stochastic interest rate

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  • Eisenberg, Julia

Abstract

We consider an insurance entity endowed with an initial capital and an income, modelled as a Brownian motion with drift. The discounting factor is modelled as a stochastic process: at first as a geometric Brownian motion, then as an exponential function of an integrated Ornstein–Uhlenbeck process. It is assumed that the insurance company seeks to maximize the cumulated value of expected discounted dividends up to the ruin time. We find an explicit expression for the value function and for the optimal strategy in the first but not in the second case, where one has to switch to the viscosity ansatz.

Suggested Citation

  • Eisenberg, Julia, 2015. "Optimal dividends under a stochastic interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 259-266.
    • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:259-266
    DOI: 10.1016/j.insmatheco.2015.10.007
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    References listed on IDEAS

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    1. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    2. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
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    Cited by:

    1. Tiziano De Angelis, 2018. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Papers 1805.12035, arXiv.org, revised Mar 2019.
    2. Julia Eisenberg & Paul Kruhner, 2016. "A Note on the Optimal Dividends Paid in a Foreign Currency," Papers 1603.07615, arXiv.org.
    3. 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.
    4. Tiziano Angelis, 2020. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Finance and Stochastics, Springer, vol. 24(1), pages 71-123, January.
    5. Elena Bandini & Tiziano De Angelis & Giorgio Ferrari & Fausto Gozzi, 2022. "Optimal dividend payout under stochastic discounting," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 627-677, April.
    6. Wujun Lv & Linlin Tian & Xiaoyi Zhang, 2023. "Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence," Mathematics, MDPI, vol. 11(13), pages 1-20, July.
    7. Linlin Tian & Xiaoyi Zhang, 2018. "Optimal Dividend of Compound Poisson Process under a Stochastic Interest Rate," Papers 1807.08081, arXiv.org.
    8. Zailei Cheng, 2017. "Optimal dividends in the dual risk model under a stochastic interest rate," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-16, March.
    9. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Papers 2108.00234, arXiv.org.
    10. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Mathematics, MDPI, vol. 9(18), pages 1-20, September.
    11. Zailei Cheng, 2017. "Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate," Papers 1705.08411, arXiv.org.
    12. Aleksandar Arandjelovi'c & Julia Eisenberg, 2024. "Reinsurance with neural networks," Papers 2408.06168, arXiv.org.
    13. Julia Eisenberg & Zbigniew Palmowski, 2020. "Optimal Dividends Paid in a Foreign Currency for a L\'evy Insurance Risk Model," Papers 2001.03733, arXiv.org.
    14. David Markantonis & G.-Fivos Sargentis & Panayiotis Dimitriadis & Theano Iliopoulou & Aimilia Siganou & Konstantina Moraiti & Maria Nikolinakou & Ilias Taygetos Meletopoulos & Nikos Mamassis & Demetri, 2023. "Stochastic Evaluation of the Investment Risk by the Scale of Water Infrastructures—Case Study: The Municipality of West Mani (Greece)," World, MDPI, vol. 4(1), pages 1-20, January.

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