The dollar falls against most major currencies; it should. But don't expect US trade deficits to fall much; in fact they could rise, since we import so much more than we export, and large corporations have gone a long way to dismantling their domestic production facilities.
Why the surging stock market, then? Imperial economics:
profits for corporations producing more and more abroad, and from our high-flying war industry.
The stock market "surge" is about as real as the troop surge in Iraq is effective. And when one fails, the other could be right behind.
Could this lead to the kind of collapse I describe in The Selfish Class? Probably not yet; financial markets will cobble something together for the time being, but the falling dollar is an indication: the "American Way of Life" is becoming unaffordable for those below the Republican-defined "middle class" with incomes of several hundred thou.