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Bounds on doubling rates of investment capital due to incorrect distributions. (English) Zbl 1168.91402
Sunada, Toshikazu (ed.) et al., Proceedings of the third Asian mathematical conference 2000, University of the Philippines, Diliman, Philippines, October 23–27, 2000. Singapore: World Scientific (ISBN 981-02-4947-0/hbk). 532-540 (2002).
Doubling rate, introduced by A. R. Barron and Th. M. Cover [IEEE Trans. Inf. Theory 34, No. 5, Part I, 1097–1100 (1988; Zbl 0662.90023)], is defined by the expectation of the logarithm of the portfolio. The difference of two doubling rates between a correct distribution and a wrong distribution is dominated by the relative entropy of these two distributions. In the present paper, the relative entropies of two multivariate normal distributions and of two distributions of the exponential families are calculated.
For the entire collection see [Zbl 0989.00018].
91B28 Finance etc. (MSC2000)