Paul A. Samuelson, Limited Liability, Short Selling, Bounded Utility, and Infinite-Variance Stable Distributions, The Journal of Financial and Quantitative Analysis, Vol. 11, No. 3 (Sep., 1976), pp. 485-503

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.

“Don't put all your eggs in one basket, ” is a familiar adage. Economists, such as Marschak, Markowitz, and Tobin, who work only with mean income and its variance, can give specific content to this rule—namely, putting a fixed total of wealth equally into independently, identically distributed investments will leave the mean gain unchanged and will minimize the variance.

Journal Article A. P. Lerner at Sixty Get access Paul A. Samuelson Paul A. Samuelson Massachusetts Institute of Technology Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 31, Issue 3, June 1964, Pages 169–178, https://doi.org/10.2307/2295906 Published: 01 June 1964

Parable and Realism in Capital Theory: The Surrogate Production Function Get access Paul A. Samuelson Paul A. Samuelson Cambridge, Mass. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 29, Issue 3, June 1962, Pages 193–206, https://doi.org/10.2307/2295954 Published: 01 June 1962

Comment Paul A. Samuelson Paul A. Samuelson Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 29, Issue 3, June 1962, Pages 251–254, https://doi.org/10.2307/2295962 Published: 01 June 1962

Journal Article Prices of Factors and Goods in General Equilibrium Get access Paul A. Samuelson Paul A. Samuelson Cambridge, Mass. Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 21, Issue 1, 1953, Pages 1–20, https://doi.org/10.2307/2296256 Published: 01 January 1953