IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v163y2014i2d10.1007_s10957-013-0445-y.html
   My bibliography  Save this article

Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model

Author

Listed:
  • Ruihua Liu

    (University of Dayton)

Abstract

This paper is concerned with an infinite-horizon problem of optimal investment and consumption with proportional transaction costs in continuous-time regime-switching models. An investor distributes his/her wealth between a stock and a bond and consumes at a non-negative rate from the bond account. The market parameters (the interest rate, the appreciation rate, and the volatility rate of the stock) are assumed to depend on a continuous-time Markov chain with a finite number of states (also known as regimes). The objective of the optimization problem is to maximize the expected discounted total utility of consumption. We first show that for a class of hyperbolic absolute risk aversion utility functions, the value function is a viscosity solution of the Hamilton–Jacobi–Bellman equation associated with the optimization problem. We then treat a power utility function and generalize the existing results to the regime-switching case.

Suggested Citation

  • Ruihua Liu, 2014. "Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 614-641, November.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-013-0445-y
    DOI: 10.1007/s10957-013-0445-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0445-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-013-0445-y?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. 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.
    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. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    2. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.

    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. Colin Atkinson & Emmeline Storey, 2010. "Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 323-357.
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    4. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678, arXiv.org.
    5. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.
    6. Guodong Ding & Daniele Marazzina, 2021. "Effect of Labour Income on the Optimal Bankruptcy Problem," Papers 2106.15426, arXiv.org.
    7. Ali Al-Aradi & Sebastian Jaimungal, 2018. "Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management," Papers 1803.05819, arXiv.org, revised Jul 2018.
    8. Kan Huang & David Simchi-Levi & Miao Song, 2012. "Optimal Market-Making with Risk Aversion," Operations Research, INFORMS, vol. 60(3), pages 541-565, June.
    9. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    10. Cayé, Thomas & Herdegen, Martin & Muhle-Karbe, Johannes, 2020. "Scaling limits of processes with fast nonlinear mean reversion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1994-2031.
    11. Alain Bensoussan & Guiyuan Ma & Chi Chung Siu & Sheung Chi Phillip Yam, 2022. "Dynamic mean–variance problem with frictions," Finance and Stochastics, Springer, vol. 26(2), pages 267-300, April.
    12. Koichi Matsumoto, 2007. "Portfolio Insurance with Liquidity Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(4), pages 363-386, December.
    13. Luitgard Veraart, 2010. "Optimal Market Making in the Foreign Exchange Market," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 359-372.
    14. Kerstin Dächert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jörg Wenzel, 2022. "Multicriteria asset allocation in practice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 349-373, June.
    15. Zuo Quan Xu & Fahuai Yi, 2014. "An Optimal Consumption-Investment Model with Constraint on Consumption," Papers 1404.7698, arXiv.org.
    16. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    17. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    18. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    19. Bruno Bouchard & Johannes Muhle-Karbe, 2018. "Simple Bounds for Transaction Costs," Working Papers hal-01711371, HAL.
    20. Romuald Elie & Ludovic Moreau & Dylan Possamai, 2017. "On a class of path-dependent singular stochastic control problems," Papers 1701.08861, arXiv.org, revised Feb 2018.

    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:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-013-0445-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.