Abstract
In a recent critical review of de Finetti’s paper “Il problema dei pieni’’, the Nobel Prize winner Harry Markowitz recognized the primacy of de Finetti in applying the mean-variance approach to finance, but pointed out that de Finetti did not solve the problem for the general case of correlated risks. We argue in this paper that a more fair sentence would be: de Finetti did solve the general problem but under an implicit hypothesis of regularity which is not always satisfied. Moreover, a natural extension of de Finetti’s procedure to non-regular cases offers a general solution for the correlation case and shows that de Finetti anticipated a modern mathematical programming approach to mean-variance problems.
Mathematics Subject Classification (2000): 91B30, 90C20
Journal of Economic Literature Classification: G11, C61, B23, D81, G22
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
1. Borch, K. (1974): The mathematical theory of insurance. Lexington Books, Lexington, MA
2. Bühlmann, H., Gerber, H. (1978): Risk bearing and the reinsurance market. The ASTIN Bulletin 10, 12–24
3. Dantzig, G.B. (1963): Linear programming and extensions. Princeton University Press, Princeton, NJ
4. de Finetti, B. (1940): Il problema dei “Pieni”. Giornale dell' Istituto Italiano degli Attuari 11, 1–88; translation (Barone, L. (2006)): The problem of full-risk insurances. Chapter I. The risk within a single accounting period. Journal of Investment Management 4(3), 19–43
5. de Finetti, B. (1969): Un matematico e l'economia. Franco Angeli, Milan
6. Karush, W. (1939): Minima of functions of several variables with inequalities as side conditions. S.M. dissertation. University of Chicago, Chicago, IL
7. Kuhn, H.W., Tucker, A.W. (1951): Nonlinear programming. In: Neyman, J. (ed.): Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, CA, pp. 481–492
8. Lintner, J. (1965): The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics 47, 13–37
9. Markowitz, H. (1952): Portfolio selection. The Journal of Finance 7, 77–91
10. Markowitz, H. (1956): The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly 3, 111–133
11. Markowitz, H. (2006): de Finetti scoops Markowitz. Journal of Investment Management 4(3), 5–18
12. Mossin, J. (1966): Equilibrium in a capital asset market. Econometrica 34, 768–783
13. Pressacco, F. (1986): Separation theorems in proportional reinsurance. Goovaerts, M. et al. (eds.): Insurance and Risk Theory. D. Reidel, Dordrecht, pp. 209-215
14. Rubinstein M. (2006a ): Bruno de Finetti and mean-variance portfolio selection. Journal of Investment Management 4(3), 3–4
15. Rubinstein M. (2006b): A history of the theory of investments. Wiley, Hoboken, NJ
16. Shapiro, J.F. (1979): Mathematical programming: structures and algorithms. Wiley-Inter-science, New York
17. Sharpe, W. (1964): Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance 19, 425–442
Author information
Authors and Affiliations
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Pressacco, F., Serafini, P. The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later. Decisions Econ Finan 30, 19–49 (2007). https://doi.org/10.1007/s10203-007-0067-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10203-007-0067-7