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The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory

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  • Ignas Gasparaviv{c}ius
  • Andrius Grigutis

Abstract

This survey article is dedicated to the life of the famous American economist H. Markowitz (1927--2023). We do revisit the main statements of the portfolio selection theory in terms of mathematical completeness including all the necessary auxiliary details.

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  • Ignas Gasparaviv{c}ius & Andrius Grigutis, 2024. "The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory," Papers 2402.10253, arXiv.org.
    • Handle: RePEc:arx:papers:2402.10253
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    References listed on IDEAS

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    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    3. Mark Rubinstein, 2002. "Markowitz's “Portfolio Selection”: A Fifty‐Year Retrospective," Journal of Finance, American Finance Association, vol. 57(3), pages 1041-1045, June.
    4. Andrius Grigutis, 2023. "Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche," Papers 2303.06148, arXiv.org.
    5. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    6. 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.
    7. Carole Bernard & Corrado De Vecchi & Steven Vanduffel, 2021. "When do two- or three-fund separation theorems hold?," Quantitative Finance, Taylor & Francis Journals, vol. 21(11), pages 1869-1883, November.
    8. André F. Perold, 2004. "The Capital Asset Pricing Model," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 3-24, Summer.
    9. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    10. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    11. Bick, Avi, 2004. "The mathematics of the portfolio frontier: a geometry-based approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 337-361, May.
    12. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    13. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    14. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
    15. Roman Vershynin, 2012. "How Close is the Sample Covariance Matrix to the Actual Covariance Matrix?," Journal of Theoretical Probability, Springer, vol. 25(3), pages 655-686, September.
    16. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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