Set an attribute to change an objects behavior, at specific times and for a specific period
Rather than making your times a dictionary indexed by an int just make it a list of tuples (start, end) and iterate through the list of trading times.
Input the list in order or sort it before starting so you can be assured that time[n].start &lt; time[n].end and time[n].end &lt; time[n+1].start.

For something as simple as your example it is clear enough what the code is doing.  It doesn't scale as you add more complexity to the decision to trade or not.  Consider different exchanges, different products, order types, etc.  Your single check_times function is going to get very complex.

To prepare for such coming complexity I would have a Trader class for each combination of things that could influence trading time, each with its own check_times function.  A Controller class would be responsible for choosing the appropriate Trader to handle things based on the attributes at hand.  Currently the only attribute you are looking at is the current time and so there would only be two Traders, and ActiveTrader and a DeactivatedTrader.

Again, depending upon the complexity of what is being implemented, these Trader's could be classes that descend from a common Trader class or could be duck-typed to have the same API.  Let Don't-Repeat-Yourself be your guide here.  If you are writing more Python code to set up the inheritance than you have saved by inheriting from a common ancestor you are doing it wrong.