IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1703.07339.html
   My bibliography  Save this paper

Stochastic control on the half-line and applications to the optimal dividend/consumption problem

Author

Listed:
  • Dariusz Zawisza

Abstract

We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations has smooth solution. The aforementioned result is used to solve the optimal dividend and consumption problem. In the proof we use a fixed point type argument, with an operator which is based on the stochastic representation for a linear equation.

Suggested Citation

  • Dariusz Zawisza, 2017. "Stochastic control on the half-line and applications to the optimal dividend/consumption problem," Papers 1703.07339, arXiv.org, revised Jul 2018.
    • Handle: RePEc:arx:papers:1703.07339
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1703.07339
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    2. Ralf Korn & Holger Kraft, 2003. "Optimal Portfolios With Defaultable Securities A Firm Value Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 793-819.
    Full references (including those not matched with items on IDEAS)

    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.
    1. Holger Kraft & Mogens Steffensen, 2006. "Portfolio problems stopping at first hitting time with application to default risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 123-150, February.
    2. Levon Avanesyan & Mykhaylo Shkolnikov & Ronnie Sircar, 2020. "Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem," Finance and Stochastics, Springer, vol. 24(4), pages 981-1011, October.
    3. Zehra Eksi & Hyejin Ku, 2017. "Portfolio optimization for a large investor under partial information and price impact," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 601-623, December.
    4. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.
    5. Jinzhu Li & Rong Wu, 2009. "Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 407-420, May.
    6. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    7. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," LIDAM Discussion Papers IRES 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    8. Marius Ascheberg & Nicole Branger & Holger Kraft & Frank Thomas Seifried, 2016. "When do jumps matter for portfolio optimization?," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1297-1311, August.
    9. Ralf Korn, 2008. "Optimal portfolios: new variations of an old theme," Computational Management Science, Springer, vol. 5(4), pages 289-304, October.
    10. Jean-Pierre Fouque & Ruimeng Hu & Ronnie Sircar, 2021. "Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market," Papers 2106.11510, arXiv.org, revised Oct 2021.
    11. Chuhao Sun & Asaf Cohen & James Stokes & Shravan Veerapaneni, 2023. "Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations," Papers 2311.12239, arXiv.org.
    12. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Financial Science Trends and Perspectives: A Review Article," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    13. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    14. Francesco Menoncin & Olivier Scaillet, 2003. "Mortality Risk and Real Optimal Asset Allocation for Pension Funds," FAME Research Paper Series rp101, International Center for Financial Asset Management and Engineering.
    15. Masaaki Fujii, 2014. "A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option pricing," CARF F-Series CARF-F-343, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Dec 2014.
    16. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.
    17. Tehranchi, Michael, 2004. "Explicit solutions of some utility maximization problems in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 109-125, November.
    18. Li, Zhongfei & Zeng, Yan & Lai, Yongzeng, 2012. "Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 191-203.
    19. T. Pang, 2004. "Portfolio Optimization Models on Infinite-Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 573-597, September.
    20. Longjie Jia & Martijn Pistorius & Harry Zheng, 2017. "Dynamic Portfolio Optimization with Looping Contagion Risk," Papers 1710.05168, arXiv.org, revised Aug 2018.

    More about this item

    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:1703.07339. 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.