IDEAS home Printed from https://ideas.repec.org/p/ofr/discus/14-01.html
   My bibliography  Save this paper

On the Optimal Wealth Process in a Log-Normal Market: Applications to Risk Management

Author

Listed:
  • Phillip Monin

    () (Office of Financial Research)

  • Thaleia Zariphopoulou

    () (The University of Texas at Austin)

Abstract

The theory of portfolio choice holds that investors balance risk and reward in their investment decisions. We explore the relationship between investors' attitudes towards taking risk and their objectives for managing the risk they take on. Working in a classical theoretical model, we calculate the distribution and density functions of an investor's optimal wealth process and prove new mathematical results for these functions under general risk preferences. By applying our results to a constant relative risk aversion investor who has a targeted value at risk or expected shortfall at a given future time, we are able to infer the investor's risk preferences and prescribe how to invest to achieve the desired goal. Then, drawing analogies to the option greeks, we define and derive closed-form expressions for "portfolio greeks," which measure the sensitivities of an investor's optimal wealth to changes in the cumulative excess stock return, time, and market parameters. Like option greeks, portfolio greeks can be used in the risk management of investors' portfolios.

Suggested Citation

  • Phillip Monin & Thaleia Zariphopoulou, 2014. "On the Optimal Wealth Process in a Log-Normal Market: Applications to Risk Management," Staff Discussion Papers 14-01, Office of Financial Research, US Department of the Treasury.
    • Handle: RePEc:ofr:discus:14-01
    as

    Download full text from publisher

    File URL: https://financialresearch.gov/staff-discussion-papers/files/OFRsdp2014-01_MoninZariphopoulou_OnOptimalWealthProcessLog-normalMarketApplicationsRiskManagement.pdf
    File Function: First version, 2014
    Download Restriction: no

    References listed on IDEAS

    as
    1. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    2. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    3. Jianming Xia, 2008. "Risk Aversion and Portfolio Selection in a Continuous-Time Model," Papers 0805.0618, arXiv.org, revised Dec 2011.
    4. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    5. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    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. Ljudmila A. Bordag, 2019. "Portfolio optimization in the case of an exponential utility function and in the presence of an illiquid asset," Papers 1910.07417, arXiv.org, revised May 2020.
    2. Wai Mun Fong, 2018. "Synthetic growth stocks," Journal of Asset Management, Palgrave Macmillan, vol. 19(3), pages 162-168, May.

    More about this item

    Keywords

    expected utility; Merton problem; value at risk (VaR); expected shortfall; portfolio greeks;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ofr:discus:14-01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gregory Feldberg) The email address of this maintainer does not seem to be valid anymore. Please ask Gregory Feldberg to update the entry or send us the correct email address. General contact details of provider: http://edirc.repec.org/data/ofrgvus.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.