While the classical Stoics did pay some attention to expectations, it was not quite in the manner that troubles you. Instead, their attention mostly focused on unexpected misfortune, because they thought that surprise makes it harder to face hardship admirably.

The classical Stoic approach would be less associated with expectations, more with assent to impressions. If you expect to become die tomorrow, or become sick, or become poor, an essential element in your being disturbed by these expectations is your belief that it would be bad to die, or become sick, or become poor. Instead, the classical Stoic would say, learn to become indifferent to all of these things, to whether you live through the day or die, to whether you are healthy or sick, to whether you are rich or poor. Yes, even the wisest still have impulses to avoid death, sickness, and poverty, but they though we could learn to recognize these impulses as illusions or good and bad.

Instead, they said, virtue is the only thing we should recognize as good. What matters is not whether we live or die, but, facing death, whether we do so honorably, or if we live, whether we use the time admirably. Note that this does not mean that they thought we shouldn't prefer life to death, or health to sickness, and act on those preferences. After all, it is only very rarely that it is more honorable to chose sickness over health, or more admirable to chose death over life. See the FAQ for more on preferred or unpreferred indifferents.

In short, focus you attention on how you live, rather than what happens to you -- how you react to your situation, rather than what situation you will have to react to.