IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v125y2019icp73-78.html
   My bibliography  Save this article

An integral equation approach for optimal investment policies with partial reversibility

Author

Listed:
  • Jeon, Junkee
  • Kim, Geonwoo

Abstract

In this paper we investigate an investment problem with partial reversibility proposed by Abel and Eberly [4] in a finite horizon. In this model, a firm can purchase capital at a given price and sell capital at a lower price. This problem can be categorized into a singular control problem and can be formulated as a Hamilton–Jacobi–Bellman(HJB) equation. Based on theoretical results in [10] and the Mellin transform techniques, we derive the coupled integral equations satisfied by the optimal investment and disinvestment boundaries, respectively. By using the recursive integration method, we solve numerically the integral equations and present the optimal investment boundary and disinvestment boundary.

Suggested Citation

  • Jeon, Junkee & Kim, Geonwoo, 2019. "An integral equation approach for optimal investment policies with partial reversibility," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 73-78.
    • Handle: RePEc:eee:chsofr:v:125:y:2019:i:c:p:73-78
    DOI: 10.1016/j.chaos.2019.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919301821
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.05.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    2. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    3. Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 581-593.
    4. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 31-62, January.
    5. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.
    6. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    7. Guo, Xin & Pham, Huyên, 2005. "Optimal partially reversible investment with entry decision and general production function," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 705-736, May.
    8. Xu, Quan & Lin, Yi & Bao, Bocheng & Chen, Mo, 2016. "Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 186-200.
    9. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    10. Maria B. Chiarolla & Ulrich G. Haussmann, 2005. "Explicit Solution of a Stochastic, Irreversible Investment Problem and Its Moving Threshold," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 91-108, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Junkee Jeon & Geonwoo Kim, 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon," Mathematics, MDPI, vol. 8(11), pages 1-10, November.
    2. Zhou Yang & Junkee Jeon, 2023. "A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization," Papers 2309.12588, arXiv.org.

    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. Junkee Jeon & Geonwoo Kim, 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon," Mathematics, MDPI, vol. 8(11), pages 1-10, November.
    2. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    3. Yiannis Kamarianakis & Anastasios Xepapadeas, 2007. "An Irreversible Investment Model with a Stochastic Production Capacity and Fixed Plus Proportional Adjustment Costs," Working Papers 0708, University of Crete, Department of Economics.
    4. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 239-271, December.
    5. Cuoco, Domenico & Liu, Hong, 2000. "Optimal consumption of a divisible durable good," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 561-613, April.
    6. 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.
    7. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    8. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    9. Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    10. Makenne, Y.L. & Kengne, R. & Pelap, F.B., 2019. "Coexistence of multiple attractors in the tree dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 70-82.
    11. Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    12. Lai, Qiang & Xu, Guanghui & Pei, Huiqin, 2019. "Analysis and control of multiple attractors in Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 192-200.
    13. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    14. Geonwoo Kim, 2020. "Valuation of Exchange Option with Credit Risk in a Hybrid Model," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    15. Laminou Abdou, Souleymane & Moraux, Franck, 2016. "Pricing and hedging American and hybrid strangles with finite maturity," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 112-125.
    16. Davis, Graham A. & Cairns, Robert D., 2017. "The odd notion of “reversible investment”," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 172-180.
    17. 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.
    18. Rama Cont & Xin Guo & Renyuan Xu, 2021. "Interbank lending with benchmark rates: Pareto optima for a class of singular control games," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1357-1393, October.
    19. Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(1), pages 25-45, March.
    20. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, 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:chsofr:v:125:y:2019:i:c:p:73-78. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.