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Efficient Portfolio Selection for Pareto-Lévy Investments*

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  • Samuelson, Paul A.

Abstract

The Markowitz analysis of efficient portfolio selection, which can be interpreted as solving the quadratic-programming problem of minimizing the variance of a normal variate subject to each prescribed mean value, easily can be generalized (in the special case of independently distributed investments) to the concave-programming problem of minimizing the “dispersion” of a stable Pareto-Lévy variate subject to each prescribed mean value. Some further generalizations involving interdependent distributions will also be presented here.

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  • Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 107-122, June.
    • Handle: RePEc:cup:jfinqa:v:2:y:1967:i:02:p:107-122_01
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    Cited by:

    1. Michael R. Powers & Thomas Y. Powers & Siwei Gao, 2012. "Risk Finance for Catastrophe Losses with Pareto‐Calibrated Lévy‐Stable Severities," Risk Analysis, John Wiley & Sons, vol. 32(11), pages 1967-1977, November.
    2. Yang, Jangho & Heinrich, Torsten & Winkler, Julian & Lafond, François & Koutroumpis, Pantelis & Farmer, J. Doyne, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," MPRA Paper 96474, University Library of Munich, Germany.
    3. Charilaos Mertzanis, 2013. "Risk Management Challenges after the Financial Crisis," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 42(3), pages 285-320, November.
    4. Cornelis A. Los, 2004. "When to Put All Your Eggs in One Basket.....When Diversification Increases Portfolio Risk!," Finance 0411037, University Library of Munich, Germany.
    5. Catherine Araujo Bonjean, 1998. "Les marchés mondiaux des produits agricoles sont-ils efficients ?," Économie rurale, Programme National Persée, vol. 243(1), pages 8-15.
    6. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    7. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    8. Jaime Alberto Vásquez & John Willmer Escobar & Diego Fernando Manotas, 2021. "AHP–TOPSIS Methodology for Stock Portfolio Investments," Risks, MDPI, vol. 10(1), pages 1-20, December.
    9. Pivato, Marcus & Seco, Luis, 2003. "Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 219-240, November.
    10. Lau, Hon-Shiang & Lau, Amy Hing Ling, 1997. "The confounding effects of distribution mixtures on some basic methods for handling stable-Paretian distributions," European Journal of Operational Research, Elsevier, vol. 100(1), pages 60-71, July.
    11. Dong Han & Fugee Tsung & Yanting Li & Jinguo Xian, 2010. "Detection of changes in a random financial sequence with a stable distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(7), pages 1089-1111.
    12. Athayde, Gustavo M. de & Flôres Junior, Renato Galvão, 2001. "Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 434, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    13. Cornelis A Los, 2005. "Why VaR FailsLong Memory and Extreme Events in Financial Markets," The IUP Journal of Financial Economics, IUP Publications, vol. 0(3), pages 19-36, September.
    14. Yaniv Konchitchki & Yan Luo & Mary L. Z. Ma & Feng Wu, 2016. "Accounting-based downside risk, cost of capital, and the macroeconomy," Review of Accounting Studies, Springer, vol. 21(1), pages 1-36, March.
    15. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).
    16. Sethi, Suresh Andrew & Reimer, Matthew & Knapp, Gunnar, 2014. "Alaskan fishing community revenues and the stabilizing role of fishing portfolios," Marine Policy, Elsevier, vol. 48(C), pages 134-141.
    17. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    18. Camilleri, Silvio John & Galea, Gabriella, 2009. "The Diversification Potential Offered by Emerging Markets in Recent Years," MPRA Paper 62491, University Library of Munich, Germany.
    19. Yang, Jangho & Heinrich, Torsten & Winkler, Julian & Lafond, François & Koutroumpis, Pantelis & Farmer, J. Doyne, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," MPRA Paper 96474, University Library of Munich, Germany.
    20. de Athayde, Gustavo M. & Flores, Renato Jr., 2004. "Finding a maximum skewness portfolio--a general solution to three-moments portfolio choice," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1335-1352, April.

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