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Vajda, Igor; Österreicher, Ferdinand

Existence, uniqueness and evaluation of log-optimal investment portfolio. (English) Zbl 0799.90013

Kybernetika 29, No. 2, 105-120 (1993).
A stock market and a log optimal investment portfolio are regarded. An if and only if condition is given for the existence of a log optimal portfolio. It is unique under the assumption that the underlying distribution of the stock market return vector is not concentrated on a hyperplane in \(\mathbb{R}^ m\) containing the diagonal. Under these assumptions deterministic and statistical approximations of log optimal portfolios are considered followed by an application to finite stock market.
Reviewer: K.Ehemann (Hamburg)

Cited in 2 Documents

MSC:

91B28 Finance etc. (MSC2000)

Keywords:

stock market; log optimal investment portfolio
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References:

[1] A. R. Barron L. Gyorfi, E. van der Meulen: Distribution estimation consistent in total variation and in two types of information divergence. IEEE Trans. Inform. Theory 38 (1992), 1437-1454. · Zbl 0765.62007 · doi:10.1109/18.149496
[2] L. Breiman: Optimal gambling systems for favouralbe games. Fourth Berkeley Symp. Math. Statist. Probab., Vol. I, Univ. Calif. Press, Berkeley 1961, pp. 65-78.
[3] T. M. Cover: An algorithm for maximizing expected log investment return. IEEE Trans. Inform. Theory 30 (1984), 369-373. · Zbl 0541.90007 · doi:10.1109/TIT.1984.1056869
[4] T. M. Cover: Universal portfolios. Mathematical Finance 16 (1991), 876-898. · Zbl 0900.90052 · doi:10.1111/j.1467-9965.1991.tb00002.x
[5] T. M. Cover, J. A. Thomas: Elements of Information Theory. Wiley, New York 1991. · Zbl 0762.94001
[6] J. Kelly: A new interpretation of information rate. Bell System Tech. J. 35 (1956), 917-926.
[7] H. A. Latane: Criteria for choice among risky ventures. Political Economy 38 (1959), 145-155.
[8] G. Morvai: Empirical log-optimal portfolio selection. Problems Control Inform. Theory 20 (1991), 453-464. · Zbl 0752.90004
[9] G. Morvai: Portfolio choice based on the empirical distribution. Kybernetika 25(1992), 484-493. · Zbl 0776.90009
[10] J. Pfanzagl: On the measurability and consistency of minimum contrast estimators. Metrika U (1969), 249-272. · Zbl 0181.45501 · doi:10.1007/BF02613654
[11] R. T. Rockafellar: Convex Analysis. Princeton Univ. Press, Princeton, N.J. 1970. · Zbl 0193.18401
[12] P. A. Samuelson: The ’fallacy’ of maximizing the geometric mean in long sequences of investing or gambling. Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 2493-2496. · Zbl 0226.62111 · doi:10.1073/pnas.68.10.2493
[13] P. A. Samuelson: Why we should not make mean log of wealth big though years to act are long. Journal of Banking and Finance 3 (1979), 305-307.
[14] S. van deGeer: The method of sieves and minimum contrast estimators. 20th European Meeting of Statisticians, Programme & Abstracts, University of Bath, September 1992, p. 243.
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