Abstract
Abstract In this paper, we mainly study the strong limit theorems for the log-optimal portfolio of the ∗-mixing stock market. First, we establish a strong limit theorem for the log-optimal portfolio of any sequence investment, then we obtain the result that the average return of the long term behavior of a sequence investment converges to the average of the expectation return in every period with probability 1 under some conditions. We also obtain another strong limit theorem for the log-optimal portfolio for a class of sequence investments. MSC:60F15, 91B28.
Highlights
This paper considers the continuous investment behaviors in the stock market under a discrete time framework
We mainly study the strong limit theorems for the log-optimal portfolio in the stock investment by using the limit properties for arbitrary random variables
We suppose that the relative prices of the stocks are a ∗-mixing sequence which is gradually independent and the investment strategy in the nth period is correlated with the information of the stock prices of the previous n – periods
Summary
This paper considers the continuous investment behaviors in the stock market under a discrete time framework. We suppose that the relative prices of the stocks are a ∗-mixing sequence which is gradually independent and the investment strategy in the nth period is correlated with the information of the stock prices of the previous n – periods. The investment of the stock is generally the long term behavior and the stock market is ∗-mixing, i.e. the stock prices in two time periods which are sufficiently far away from each other can be approached as being independent.
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