Translation Invariance of Investment

英文摘要：

For a game with positive profit, the optimal proportion of investment required to continue investing without borrowing is uniquely determined by an integral equation for each price. For a game with parallel translated profit, the ratio of the optimal proportion of investment to its price has some invariance properties. The optimal price of a game with parallel translated profit converges to its expectation divided by e to the riskless interest rate for a certain period.