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Optimising dividends and consumption under an exponential CIR as a discount factor

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Listed:
  • Julia Eisenberg

    (TU Wien)

  • Yuliya Mishura

    (Taras Shevchenko National University of Kyiv)

Abstract

We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spending/dividend payments under a discounting factor given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we are able to show that for a special parameter choice the optimal strategy is a constant-barrier strategy.

Suggested Citation

  • Julia Eisenberg & Yuliya Mishura, 2020. "Optimising dividends and consumption under an exponential CIR as a discount factor," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 285-309, October.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00714-w
    DOI: 10.1007/s00186-020-00714-w
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    References listed on IDEAS

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    1. Akyildirim, Erdinç & Güney, I. Ethem & Rochet, Jean-Charles & Soner, H. Mete, 2014. "Optimal dividend policy with random interest rates," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 93-101.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. 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.
    5. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
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