IDEAS home Printed from
   My bibliography  Save this paper

Optimal investment policy and dividend payment strategy in an insurance company


  • Pablo Azcue
  • Nora Muler


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,
  • Handle: RePEc:arx:papers:1010.4988

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

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


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

    Cited by:

    1. Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747,, revised Feb 2014.
    2. 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.
    3. repec:spr:joptap:v:159:y:2013:i:1:d:10.1007_s10957-012-0263-7 is not listed on IDEAS
    4. repec:eee:insuma:v:74:y:2017:i:c:p:31-45 is not listed on IDEAS
    5. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1251-3 is not listed on IDEAS
    6. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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.

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

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.