IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v35y2020i2p43-55n4.html
   My bibliography  Save this article

A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics

Author

Listed:
  • Baten Md. Azizul

    (Department of Statistics, School of Physical Sciences, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh)

  • Khalid Ruzelan

    (Institute of Strategic Industrial Decision Modelling, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia)

Abstract

This study considers a stochastic control model in which an economic unit has productive capital and liabilities in the form of debt. The worth of capital changes over time through investment and random Brownian fluctuations in the unit price of capital. Income from production is also subject to the random Brownian fluctuations. The existence of the solutions to the associated Hamilton Jacobi Bellman equation for this model is established and the optimal policies are characterized. The optimal advertising rate as a function of the market share, the optimal consumption rate and the fraction of the wealth invested in stock at any time are obtained. The worth of the capital and the optimal consumption policy are derived for the stochastic optimal investment consumption model associated with the Hamilton Jacobi Bellman equation. Analysis and numerical simulations are then presented.

Suggested Citation

  • Baten Md. Azizul & Khalid Ruzelan, 2020. "A Stochastic Control Model of Investment and Consumption with Applications to Financial Economics," Stochastics and Quality Control, De Gruyter, vol. 35(2), pages 43-55, December.
    • Handle: RePEc:bpj:ecqcon:v:35:y:2020:i:2:p:43-55:n:4
    DOI: 10.1515/eqc-2020-0017
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/eqc-2020-0017
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/eqc-2020-0017?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. Dockner, Engelbert J & Feichtinger, Gustav, 1993. "Cyclical Consumption Patterns and Rational Addiction," American Economic Review, American Economic Association, vol. 83(1), pages 256-263, March.
    2. T. Pang, 2004. "Portfolio Optimization Models on Infinite-Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 573-597, September.
    3. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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. Minglian Lin & Indranil SenGupta, 2021. "Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model," Papers 2104.06293, arXiv.org.
    2. Najafi, Amir Abbas & Pourahmadi, Zahra, 2016. "An efficient heuristic method for dynamic portfolio selection problem under transaction costs and uncertain conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 154-162.
    3. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    4. Tao Pang & Katherine Varga, 2019. "Portfolio Optimization for Assets with Stochastic Yields and Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 691-729, August.
    5. Anne Lavigne, 2006. "Gouvernance et investissement des fonds de pension privés aux Etats-Unis," Working Papers halshs-00081401, HAL.
    6. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    7. Alan J. Auerbach, 1981. "Evaluating the Taxation of Risky Assets," NBER Working Papers 0806, National Bureau of Economic Research, Inc.
    8. Hong, Claire Yurong & Lu, Xiaomeng & Pan, Jun, 2021. "FinTech adoption and household risk-taking," BOFIT Discussion Papers 14/2021, Bank of Finland Institute for Emerging Economies (BOFIT).
    9. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    10. Auffret, Philippe, 2001. "An alternative unifying measure of welfare gains from risk-sharing," Policy Research Working Paper Series 2676, The World Bank.
    11. Chen, An & Hieber, Peter & Sureth, Caren, 2022. "Pay for tax certainty? Advance tax rulings for risky investment under multi-dimensional tax uncertainty," arqus Discussion Papers in Quantitative Tax Research 273, arqus - Arbeitskreis Quantitative Steuerlehre.
    12. Mayank Goel & Suresh Kumar K., 2006. "A Risk-Sensitive Portfolio Optimisation Problem with Stochastic Interest Rate," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 5(3), pages 263-282, December.
    13. Andreas Fagereng & Luigi Guiso & Davide Malacrino & Luigi Pistaferri, 2020. "Heterogeneity and Persistence in Returns to Wealth," Econometrica, Econometric Society, vol. 88(1), pages 115-170, January.
    14. Yuqian Xu & Lingjiong Zhu & Michael Pinedo, 2020. "Operational Risk Management: A Stochastic Control Framework with Preventive and Corrective Controls," Operations Research, INFORMS, vol. 68(6), pages 1804-1825, November.
    15. Yuki SHIGETA, 2022. "A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models:A Case of Regular Controls under Markov Chain Uncertainty," Discussion papers e-22-009, Graduate School of Economics , Kyoto University.
    16. John H. Cochrane, 1999. "New facts in finance," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 23(Q III), pages 36-58.
    17. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    18. Mr. Christopher Carroll & Mr. Martin Sommer & Mr. Jiri Slacalek, 2012. "Dissecting Saving Dynamics: Measuring Wealth, Precautionary, and Credit Effects," IMF Working Papers 2012/219, International Monetary Fund.
    19. Bihary, Zsolt & Víg, Attila András, 2018. "Portfólióallokáció csődveszély esetén, korlátolt felelősség mellett [Portfolio allocation in case of failure risk in the presence of limited liability]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 711-725.
    20. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.

    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:bpj:ecqcon:v:35:y:2020:i:2:p:43-55:n:4. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.