IDEAS home Printed from https://ideas.repec.org/a/cuf/journl/y2003v4i2p427-469.html
   My bibliography  Save this article

A Wealth-Dependent Investment Opportunity Set: Its Effect on Optimal Consumption and Portfolio Decisions

Author

Listed:
  • Sungsub Choi

    (Department of Mathematics, Pohang University of Science and Technology)

  • Hyeng Keun Koo

    (School of Business Administration, Ajou University)

  • Gyoocheol Shim

    (Department of Mathematics, Pohang University of Science and Technology)

  • Thaleia Zariphopoulou

    (Department of Mathematics, University of Texas at Austin)

Abstract

We consider a consumption and investment problem where an investor¡¯s investment opportunity gets enlarged when she becomes rich enough, i.e., when her wealth touches a critical level. We derive optimal consumption and investment rules assuming that the investor has a time-separable von Neumann-Morgenstern utility function. An interesting feature of optimal rules is that the investor consumes less and takes more risk in risky assets if the investor expects that she will have a better investment opportunity when her wealth reaches a critical level.

Suggested Citation

  • Sungsub Choi & Hyeng Keun Koo & Gyoocheol Shim & Thaleia Zariphopoulou, 2003. "A Wealth-Dependent Investment Opportunity Set: Its Effect on Optimal Consumption and Portfolio Decisions," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 427-469, November.
    • Handle: RePEc:cuf:journl:y:2003:v:4:i:2:p:427-469
    as

    Download full text from publisher

    File URL: http://www.aeconf.net/Articles/Nov2003/aef040208.pdf
    Download Restriction: no
    File URL: http://down.aefweb.net/AefArticles/aef040208.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Lehoczky & S. Sethi & S. Shreve, 1983. "Optimal Consumption and Investment Policies Allowing Consumption Constraints and Bankruptcy," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 613-636, November.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    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.
    4. Ioannis Karatzas & John P. Lehoczky & Suresh P. Sethi & Steven E. Shreve, 1986. "Explicit Solution of a General Consumption/Investment Problem," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 261-294, May.
    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. Choi, Sungsub & Kim, Sungjun & Shim, Gyoocheol, 2016. "Effect of lifetime uncertainty on consumption/investment with luxury bequest motives," Finance Research Letters, Elsevier, vol. 17(C), pages 275-279.

    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. Martin Herdegen & David Hobson & Joseph Jerome, 2021. "An elementary approach to the Merton problem," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1218-1239, October.
    2. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2002. "An approximation algorithm for optimal consumption/investment problems," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 55-69, April.
    3. Dongchen Li & Virginia R. Young, 2020. "Maximizing expected exponential utility of consumption with a constraint on expected time in poverty," Annals of Finance, Springer, vol. 16(1), pages 63-99, March.
    4. Martin Herdegen & David Hobson & Joseph Jerome, 2020. "An elementary approach to the Merton problem," Papers 2006.05260, arXiv.org, revised Mar 2021.
    5. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    6. A. Cadenillas & S. P. Sethi, 1997. "Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 243-272, May.
    7. Kyoung Jin Choi & Hyeng Keun Koo & Do Young Kwak, 2004. "Optimal Stopping of Active Portfolio Management," Annals of Economics and Finance, Society for AEF, vol. 5(1), pages 93-126, May.
    8. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    9. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    10. Adriana Ocejo, 2018. "Explicit solutions to utility maximization problems in a regime-switching market model via Laplace transforms," Papers 1804.08442, arXiv.org.
    11. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    12. Svensson, L.E.O., 1988. "Portfolio Choice And Asset Pricing With Nontraded Assets," Papers 417, Stockholm - International Economic Studies.
    13. Tina Engler & Alfons Balmann, 2015. "On Investment Consumption Modeling with Jump Process Extensions for Productive Sectors," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 949-958, December.
    14. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2020. "A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies," Papers 2012.06703, arXiv.org, revised May 2021.
    15. Kyoung Jin Choi & Gyoocheol Shim & Yong Hyun Shin, 2008. "Optimal Portfolio, Consumption‐Leisure And Retirement Choice Problem With Ces Utility," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 445-472, July.
    16. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.
    17. James J. Kung, 2014. "Optimal Portfolio Decision Rule Under Nonparametric Characterization of the Interest Rate Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 225-238, April.
    18. Kenneth C. Lichtendahl & Raul O. Chao & Samuel E. Bodily, 2012. "Habit Formation from Correlation Aversion," Operations Research, INFORMS, vol. 60(3), pages 625-637, June.
    19. Sona Kilianova & Daniel Sevcovic, 2013. "Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem," Papers 1307.3672, arXiv.org, revised Jul 2013.
    20. James Kung, 2008. "Dynamic strategies for fixed-income investment," Applied Economics, Taylor & Francis Journals, vol. 40(10), pages 1341-1354.

    More about this item

    Keywords

    Consumption; Investment; Utility function; Brownian motion; Optimal strategy; Investment opportunity; Critical wealth level;
    All these keywords.

    JEL classification:

    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:cuf:journl:y:2003:v:4:i:2:p:427-469. 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: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    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.