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The dividend problem with a finite horizon

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  • Tiziano De Angelis
  • Erik Ekstrom

Abstract

We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at $0$ and created at a rate proportional to its local time.

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  • Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1609.01655
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    References listed on IDEAS

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    1. Boetius, Frederik & Kohlmann, Michael, 1998. "Connections between optimal stopping and singular stochastic control," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 253-281, September.
    2. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    3. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2014. "A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries," Papers 1405.2442, arXiv.org, revised Nov 2014.
    4. Peter Grandits, 2015. "An optimal consumption problem in finite time with a constraint on the ruin probability," Finance and Stochastics, Springer, vol. 19(4), pages 791-847, October.
    5. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    6. Duistermaat, J.J. & Kyprianou, A.E. & van Schaik, K., 2005. "Finite expiry Russian options," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 609-638, April.
    7. M. I. Taksar, 1985. "Average Optimal Singular Control and a Related Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 63-81, February.
    8. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    9. Radner, Roy & Shepp, Larry, 1996. "Risk vs. profit potential: A model for corporate strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1373-1393, August.
    10. de Angelis, Tiziano & Ferrari, Giorgio, 2016. "Stochastic nonzero-sum games: a new connection between singular control and optimal stopping," Center for Mathematical Economics Working Papers 565, Center for Mathematical Economics, Bielefeld University.
    11. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, April.
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    Cited by:

    1. Yan, Tingjin & Park, Kyunghyun & Wong, Hoi Ying, 2022. "Irreversible reinsurance: A singular control approach," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 326-348.
    2. Tiziano De Angelis, 2018. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Papers 1805.12035, arXiv.org, revised Mar 2019.
    3. Kristoffer Lindensjö & Filip Lindskog, 2020. "Optimal dividends and capital injection under dividend restrictions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 461-487, December.
    4. Zhang, Jiannan & Chen, Ping & Jin, Zhuo & Li, Shuanming, 2021. "On a class of non-zero-sum stochastic differential dividend games with regime switching," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. D'Auria, Bernardo & Guada, Abel, 2021. "Some results on optimally exercising American put options for time-inhomogeneous processes," DES - Working Papers. Statistics and Econometrics. WS 33130, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Ferrari, Giorgio & Zhu, Shihao, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Center for Mathematical Economics Working Papers 683, Center for Mathematical Economics, Bielefeld University.
    7. Giorgio Ferrari & Shihao Zhu, 2023. "Optimal Retirement Choice under Age-dependent Force of Mortality," Papers 2311.12169, arXiv.org.
    8. Giorgio Ferrari & Patrick Schuhmann, 2018. "An Optimal Dividend Problem with Capital Injections over a Finite Horizon," Papers 1804.04870, arXiv.org, revised May 2019.
    9. 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.
    10. 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.
    11. Tiziano Angelis & Gabriele Stabile, 2019. "On the free boundary of an annuity purchase," Finance and Stochastics, Springer, vol. 23(1), pages 97-137, January.
    12. Ferrari, Giorgio & Schuhmann, Patrick, 2018. "An Optimal Dividend Problem with Capital Injections over a Finite Horizon," Center for Mathematical Economics Working Papers 595, Center for Mathematical Economics, Bielefeld University.
    13. Ernst, Philip A. & Imerman, Michael B. & Shepp, Larry & Zhou, Quan, 2022. "Fiscal stimulus as an optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1091-1108.
    14. Tiziano De Angelis & Alessandro Milazzo, 2019. "Optimal stopping for the exponential of a Brownian bridge," Papers 1904.00075, arXiv.org, revised Nov 2019.
    15. Giorgio Ferrari & Shihao Zhu, 2022. "On a Merton Problem with Irreversible Healthcare Investment," Papers 2212.05317, arXiv.org, revised Dec 2023.
    16. Cheng Cai & Tiziano De Angelis, 2021. "A change of variable formula with applications to multi-dimensional optimal stopping problems," Papers 2104.05835, arXiv.org, revised Jul 2023.
    17. Cai, Cheng & De Angelis, Tiziano, 2023. "A change of variable formula with applications to multi-dimensional optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 33-61.
    18. Ferrari, Giorgio & Zhu, Shihao, 2022. "Consumption Descision, Portfolio Choice and Healthcare Irreversible Investment," Center for Mathematical Economics Working Papers 671, Center for Mathematical Economics, Bielefeld University.

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