IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1010.4988.html
   My bibliography  Save this paper

Optimal investment policy and dividend payment strategy in an insurance company

Author

Listed:
  • Pablo Azcue
  • Nora Muler

Abstract

We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cram\'{e}r--Lundberg process. The firm has the option of investing part of the surplus in a Black--Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the smallest viscosity solution of the associated second-order integro-differential Hamilton--Jacobi--Bellman equation. We study the regularity of the optimal value function. We show that the optimal dividend payment strategy has a band structure. We find a method to construct a candidate solution and obtain a verification result to check optimality. Finally, we give an example where the optimal dividend strategy is not barrier and the optimal value function is not twice continuously differentiable.

Suggested Citation

  • Pablo Azcue & Nora Muler, 2010. "Optimal investment policy and dividend payment strategy in an insurance company," Papers 1010.4988, arXiv.org.
    • Handle: RePEc:arx:papers:1010.4988
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1010.4988
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. P. Sethi & N. A. Derzko & J. P. Lehoczky, 1991. "A Stochastic Extension of the Miller‐Modigliani Framework1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 57-76, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yan Wang & Lei Wang & Kok Lay Teo, 2018. "Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 501-532, November.
    2. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    3. Josef Anton Strini & Stefan Thonhauser, 2019. "On a dividend problem with random funding," Papers 1901.06309, arXiv.org.
    4. Zhou, Zhou & Jin, Zhuo, 2020. "Optimal equilibrium barrier strategies for time-inconsistent dividend problems in discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 100-108.
    5. Ying Shen & Chuancun Yin & Kam Chuen Yuen, 2011. "Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes," Papers 1101.0446, arXiv.org, revised Feb 2014.
    6. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747, arXiv.org, revised Feb 2014.
    7. Philipp Lukas Strietzel & Henriette Elisabeth Heinrich, 2022. "Optimal Dividends for a Two-Dimensional Risk Model with Simultaneous Ruin of Both Branches," Risks, MDPI, vol. 10(6), pages 1-23, June.
    8. Zhuo Jin & Huafu Liao & Yue Yang & Xiang Yu, 2019. "Optimal Dividend Strategy for an Insurance Group with Contagious Default Risk," Papers 1909.09511, arXiv.org, revised Oct 2020.
    9. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    10. Andrea Barth & Santiago Moreno–Bromberg & Oleg Reichmann, 2016. "A Non-stationary Model of Dividend Distribution in a Stochastic Interest-Rate Setting," Computational Economics, Springer;Society for Computational Economics, vol. 47(3), pages 447-472, March.
    11. Yoshioka, Hidekazu & Yaegashi, Yuta, 2019. "A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 40-66.
    12. Zhuo Jin & G. Yin, 2013. "Numerical Methods for Optimal Dividend Payment and Investment Strategies of Markov-Modulated Jump Diffusion Models with Regular and Singular Controls," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 246-271, October.
    13. Chen, Shumin & Zeng, Yan & Hao, Zhifeng, 2017. "Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 31-45.
    14. Linlin Tian & Lihua Bai & Junyi Guo, 2020. "Optimal Singular Dividend Problem Under the Sparre Andersen Model," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 603-626, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      More about this item

      NEP fields

      This paper has been announced in the following NEP Reports:

      Statistics

      Access and download statistics

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1010.4988. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.