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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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    1. Catherine Araujo Bonjean, 1998. "Les marchés mondiaux des produits agricoles sont-ils efficients ?," Économie rurale, Programme National Persée, vol. 243(1), pages 8-15.
    2. 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.
    3. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    4. 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).
    5. 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.
    6. 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.
    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    8. Camilleri, Silvio John & Galea, Gabriella, 2009. "The Diversification Potential Offered by Emerging Markets in Recent Years," MPRA Paper 62491, University Library of Munich, Germany.
    9. Lafond, François & Farmer, J. Doyne & Koutroumpis, Pantelis & Winkler, Julian & Heinrich, Torsten & Yang, Jangho, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," INET Oxford Working Papers 2019-14, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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).
    19. 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.

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