IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v86y2000i2p323-343.html
   My bibliography  Save this article

Singular stochastic control in the presence of a state-dependent yield structure

Author

Listed:
  • Alvarez, Luis H. R.

Abstract

We consider the determination of the optimal singular stochastic control for maximizing the expected cumulative revenue flows in the presence of a state-dependent marginal yield measuring the instantaneous returns accrued from irreversibly exerting the singular policy. As in standard models of singular stochastic control, the underlying stochastic process is assumed to evolve according to a regular linear diffusion. We derive the value of the optimal strategy by relying on a combination of stochastic calculus, the classical theory of diffusions, and non-linear programming. We state a set of usually satisfied conditions under which the optimal policy is to reflect the controlled process downwards at an optimal threshold satisfying an ordinary first-order necessary condition for an optimum. We also consider the comparative static properties of the value and state a set of sufficient conditions under which it is concave. As a consequence, we are able to state a set of sufficient conditions under which the sign of the relationship between the volatility of the process and the value is negative.

Suggested Citation

  • Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 323-343, April.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:2:p:323-343
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00102-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Federico, Salvatore & Ferrari, Giorgio & Schuhmann, Patrick, 2019. "A Model for the Optimal Management of Inflation," Center for Mathematical Economics Working Papers 624, Center for Mathematical Economics, Bielefeld University.
    2. Federico, Salvatore & Ferrari, Giorgio & Riedel, Frank & Röckner, Michael, 2024. "Variational Inequalities and Smooth-Fit Principle for Singular Stochastic Control Problems in Hilbert Spaces," Center for Mathematical Economics Working Papers 692, Center for Mathematical Economics, Bielefeld University.
    3. Ferrari, Giorgio & Koch, Torben, 2018. "An optimal extraction problem with price impact," Center for Mathematical Economics Working Papers 603, Center for Mathematical Economics, Bielefeld University.
    4. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," LIDAM Discussion Papers CORE 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    6. Zhuo Jin & George Yin & Chao Zhu, 2011. "Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation," Papers 1111.2584, arXiv.org.
    7. Ferrari, Giorgio, 2018. "On a Class of Singular Stochastic Control Problems for Reflected Diffusions," Center for Mathematical Economics Working Papers 592, Center for Mathematical Economics, Bielefeld University.
    8. Salvatore Federico & Giorgio Ferrari & Patrick Schuhmann, 2019. "A Model for the Optimal Management of Inflation," Department of Economics University of Siena 812, Department of Economics, University of Siena.
    9. 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.
    10. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    11. Giorgio Ferrari & Torben Koch, 2018. "An Optimal Extraction Problem with Price Impact," Papers 1812.01270, arXiv.org.
    12. Nuno M. Brites, 2022. "Optimal Harvesting of Stochastically Fluctuating Populations Driven by a Generalized Logistic SDE Growth Model," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    13. Alvarez E., Luis H.R. & Hening, Alexandru, 2022. "Optimal sustainable harvesting of populations in random environments," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 678-698.
    14. Ky Q. Tran & Bich T. N. Le & George Yin, 2022. "Harvesting of a Stochastic Population Under a Mixed Regular-Singular Control Formulation," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1106-1132, December.

    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:eee:spapps:v:86:y:2000:i:2:p:323-343. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.