Abstract—In this paper, the expectation of the reciprocal of first-degree polynomials of non-negative valued random variables is calculated. This is motivated to compute the Kelly criterion, which is the optimal solution of the maximization of the expected logarithm of the investment return. As soon as the expectation of the reciprocal of first-degree polynomials of asset returns is calculated, which is our main interest, the Kelly criterion can be obtained by using the ordinary optimization technique or applying the appropriate algorithm.
Index Terms—Expectation, probability, investment strategy, Kelly criterion.
N. Yoshida is with the Faculty of Science and Engineering, Chuo University, Tokyo, 112-8551 Japan (e-mail: kelly-oper.calc.05t@g.chuo-u.ac.jp).
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Cite:Naohiro Yoshida, "On Calculating Method of the Kelly Criterion for Financial Investment in Single Risky Asset with Various Distributions of Returns," International Journal of Modeling and Optimization vol. 11, no. 2, pp. 42-46, 2021.
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