Suppose you have \$10,000 and want to invest in the stock market. You initially buy 500 shares of DGCo (Don't Gamble Inc), at \$10 each. Assume that you trade every day, even on Sundays, and you buy 10 shares of DGCo every time that it goes up by \$1 in price, and sell 10 shares every time it goes down by \$1 in price. Assume that the price of the stock is a random variable and that it is equally likely that at any time it will go up by \$1 or down by $1.
Compute the expected amount of money that you will have after trading for a year this way.
I'm familiar with the expected value definition, but I think this one is difficult because I think all days must be correlated, the amount of money you have on day t depends on what happens on all previous days. But maybe I'm overthinking it, please help.
I hope you can help me with this problem, I'm very confused.