Let's suppose you start with $1000 to invest, and the only thing you can invest it in is stock ABC. You are only permitted to occupy two states:

* All assets in cash

* All assets in stock ABC

You incur a $2 transaction fee every time you buy or sell.

Kind of annoying limitations to operate under. But you have a powerful advantage as well. You have a perfect crystal ball that each day gives you the [probability density function](http://en.wikipedia.org/wiki/Probability_density_function) of ABC's closing price for the following day (but no further ahead in time).

What would be an optimal decision rule for when to buy and sell?