Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T07:18:07.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on “Optimal Growth Portfolios When Yields are Serially Correlated”

Published online by Cambridge University Press:  19 October 2009

William T. Ziemba
Get access Rights & Permissions [Opens in a new window]

Extract

In [2] Hakansson and Liu presented a multiperiod portfolio model in which there is an optimal myopic policy. In particular, at any decision point j and state m the optimal amount to invest in opportunity i, namely , may be found by maximizing

(42a)

subject to

(42b)

(42c) ,

where the expectation is taken with respect to the β's, and the p's and r are positive constants (r > 1). Assumptions are made in [2] which guarantee that (42) has a unique optimal solution and that the set of vijm which satisfies (42b and 42c) is a nonempty, compact, convex set for all j and m.

Type
Communications
Information
Journal of Financial and Quantitative Analysis , Volume 7 , Issue 4 , September 1972 , pp. 1995 - 2000
Copyright
Copyright © School of Business Administration, University of Washington 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Davis, P.J., and Rabinowitz, P.. Numerical Integration. Waltham, Mass.: Blaisdell Publishing Co., 1967.Google Scholar
[2]Hakansson, Nils H., and Liu, Tien-Ching. “Optimal'Growth Portfolios When Yields Are Serially Correlated.” Review of Economics and Statistics, LII, 1970, pp. 385–394.CrossRefGoogle Scholar
[3]Hakansson, Nils H. “Risk Disposition and the Separation Property in Portfolio Selection.” Journal of Financial and Quantitative Analysis, IV, 1969, pp. 401–416.Google Scholar
[4]Hakansson, Nils H. “Optimal Entrepreneurial Decisions in a Completely Stochastic Environment.” Management Science, XVII, 1971, pp. 427–449.Google Scholar
[5]Hakansson, Nils H. “Capital Growth and the Mean-Variance Approach to Portfolio Selection.” Journal of Financial and Quantitative Analysis, VI, 1971, pp. 517–557.CrossRefGoogle Scholar
[6]Loève, M.Probability Theory, 3rd ed.Princeton, N.J.: Van Nostrand Publishing Co., 1963.Google Scholar
[7]McCormick, G.P. “Anti-Zig-Zagging by Bending.” Management Science, XV, 1969, pp. 315–320.Google Scholar
[8]McCormick, G.P. “The Variable Reduction Method for Nonlinear Programming.” Management Science, XVII, 1970, pp. 146–160.Google Scholar
[9]Zangwill, W.I.Nonlinear Programming: A Unified Approach. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1969.Google Scholar
[10]Ziemba, W.T. “Computational Algorithms for Convex Stochastic Programs with Simple Recourse.” Operations Research, XVIII, 1970, pp. 414–431.CrossRefGoogle Scholar
[11]Ziemba, W.T. “Solving Nonlinear Programming Problems with Stochastic objective Functions.” Journal of Financial and Quantitative Analysis, VII, 1972, pp. 1809–1827.Google Scholar