Which branch of psychology deals with decision making under stress? Our decisions are usually based on a system of perspectives, which in turn are based on one's own set of values. However there are traumatizing situations where this system of perspectives is turned completely upside down forcing us to make decisions that may look irrational (or that are really irrational due to emotional and other mental factors eg. panic).

Which branch of psychology deals with the subject of how different unexpected inputs affect our decision making process?
Decision-making or decision theory is its own subdiscipline under cognitive science (also often studied by statisticians, philosophers, economists, and faculty in business schools). Within this discipline, understanding how stress affects your behavior is very important and not understudied area. For a recent survey with a neurobiological focus, see:

Starcke, K., &amp; Brand, M. (2012). Decision making under stress: A selective review. Neuroscience &amp; Biobehavioral Reviews, 36(4), 1228-1248.

Of course, stress and decision making is not restricted to humans. It is also studied in a purely biological setting. For a survey focusing on predation, see:

Lima, S. L. (1998). Stress and decision making under the risk of predation: recent developments from behavioral, reproductive, and ecological perspectives. Advances in the Study of Behavior, 27, 215-290.