Undetermined unless you specify my utility function. Would, for example, I prefer having $1000, with certainty or having a 50% chance of $900 and a 50% chance of $1200; also how much do I care about the future? Also, even though my crystal ball works only for the following day, I still must have some beliefs about what will happen in the future.
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?