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The analysis of risky portfolios by geometric programming

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Summary

The problem of selecting a portfolio from a set of risky business ventures is considered. It is formulated as a maximization of the risk-adjusted (certainty-equivalent) profit for the portfolio based upon the exponential utility function and analysed via generalised geometric programming. Generalised geometric programming provides dual programs for the general case and for particular probability distributions. The particular cases of gamma, binomial, and normal distributions are converted into duals which arc of one dimension regardless of the number of portfolios.

Zusammenfassung

Ausgangspunkt dieses Aufsatzes ist das folgende Portfolio-Problem: Ein gegebenes Budget ist auf verschiedene Anlagemöglichkeiten so aufzuteilen, daß dabei der erwartete Nutzen des Gesamtertrages maximiert wird. Dieses Problem wird — zunächst ohne Verwendung einer Wahrscheinlichkeitsverteilung für die Erträge der einzelnen Anlagemöglichkeiten — mit Hilfe der verallgemeinerten geometrischen Programmierung analysiert. Es werden duale Programme abgeleitet, die die Lösung des Portfolio-Problems für verschiedene spezielle Verteilungsfunktionen in sehr einfacher Weise gestatten.

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Authors and Affiliations

  1. School of Mechanical and Industrial Engineering, University of New South Wales, 2033, Kensington, N.S.W., Australia

    T. R. Jefferson & C. H. Scott

  2. The Wharton School, University of Pennsylvania, 19104, Philadelphia, Pennsylvania, USA

    J. M. Cozzolino

Authors
  1. T. R. Jefferson
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  2. C. H. Scott
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  3. J. M. Cozzolino
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Jefferson, T.R., Scott, C.H. & Cozzolino, J.M. The analysis of risky portfolios by geometric programming. Zeitschrift für Operations Research 23, 207–217 (1979). https://doi.org/10.1007/BF01919485

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  • DOI: https://doi.org/10.1007/BF01919485

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