IDEAS home Printed from https://ideas.repec.org/p/sce/scecf1/240.html
   My bibliography  Save this paper

Portfolio Selection Models Driven by Non Gaussian Price Dynamics

Author

Listed:
  • Marina Resta

Abstract

Since the beginning of this century, the normal distribution has played a central role in the mathematical finance literature. However, major drawbacks insight this assumption rely in the absence of closed form expressions for both its cumulative and probability density functions. Additionally, although a great deal of efforts have been spent along the past decades to prove the empirical consistency of this assumption, real data have often offered a contrasting evidence, that is the exhibition of heavy tails and skewness.This paper starts from this point to consider the classical Merton problem of optimal portfolio selection and consumption, when alternatives to standard Brownian Motion are considered to model stock price dynamics. In particular, two directions will be spanned: a)\tthe Benth , Karlsen and Reikvam approach 2 (BKR since now on), who studied the underlying optimisation problem within a viscosity solution framework. The systematic solution provided by the authors relies on the possibility to replace the standard model for stock prices in the Black-Scholes world with one assuming the underlying process to belong to the class of Levy distributions. Hence the optimisation problem is solved via the corresponding Hamilton-Jacobi-Bellman equation, by weakening conditions requested . Since now only theoretical prove for the inverse Gaussian distribution case is given. A primer aim of this paper is, therefore, to test whether or not the above method can be extended to the class of Levy stable processes well known in economics, and hence to test empirically the plausibility of BKR method once a real stock to fit the model is chosen under different assumptions over distributions. b)\tA neural net approach, Ïletting the data to speak for themselvesÓ, which uses the properties of Self Organising Features maps to reconstruct features of high dimensional input into reduced dimensional space. The outline of the paper is as follows: section I introduces Merton problem within both traditional Brownian motion and BKR model assumption; section II describes the numerical solution adopted in this paper to model BKR approach; in section III the neural approach will be discussed. Section IV will focus on simulation results, under different assumptions over risk aversion and interest rates. Finally, section V will give some conclusions and outlooks for future works.

Suggested Citation

  • Marina Resta, 2001. "Portfolio Selection Models Driven by Non Gaussian Price Dynamics," Computing in Economics and Finance 2001 240, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:240
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    Keywords

    Merton Problem; Non-Gaussian World; Self Organizing Maps;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G19 - Financial Economics - - General Financial Markets - - - Other

    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:sce:scecf1:240. 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: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.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.

    We have no references for this item. You can help adding them by using 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.