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Portfolio Selection Models Driven by Non Gaussian Price Dynamics


  • Marina Resta


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

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    References listed on IDEAS

    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Andersson, Michael K. & Gredenhoff, Mikael P., 1999. "On the maximum likelihood cointegration procedure under a fractional equilibrium error," Economics Letters, Elsevier, vol. 65(2), pages 143-147, November.
    3. Baillie, Richard T & Bollerslev, Tim, 1994. " Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    4. Tsay, Wen-Jen, 2000. "Estimating Trending Variables In The Presence Of Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 16(03), pages 324-346, June.
    5. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
    6. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    8. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    10. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
    11. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    12. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    13. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    14. Abul M.M. Masih & Rumi Masih, 1998. "A Fractional Cointegration Approach to Testing Mean Reversion Between Spot and Forward Exchange Rates: A Case of High Frequency Data with Low Frequency Dynamics," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 25(7&8), pages 987-1003.
    15. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    16. Marinucci, D & Robinson, Peter M., 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
    17. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    18. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    19. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.
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    More about this item


    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


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