Investment and risk always go together. Namely, the high investment rate of return is followed by the high risk. Therefore, we need to take a proper measure to minimize the risk and simultaneously to maximize the investment rate of return. To solve and optimize this problem, we hedge the risk using the diversified investment instead of the entire investment at a time. Accordingly, we determine the optimal allocation of the investment capital to minimize the investment risk. In this paper, we discuss the Kelly criterion. The Kelly criterion is adopted to determine the optimal fixed fraction that is contributed to maximizing the geometric mean of the return over a long period of time. The criterion is implemented with the concept of the flaws of averages, especially with the Jensen`s inequality assuming that the function employed has a type of convexity. Finally, we illustrate it with a numerical example. |