In daily life we are constantly faced with decisions that have uncertain outcomes. This uncertainty can lead to feelings of anxiety. However, the reciprocal role that anxiety plays in altering the decisions made under uncertainty is not fully understood. This is important, because psychological treatments for anxiety disorders attempt to alter anxiety-related decision-making. In this study we therefore probed the computational basis of decision-making under uncertainty in individuals with high levels of mood and anxiety symptoms. Specifically, healthy individuals (N=88) and individuals with mood and anxiety disorders (N=44) were asked to choose between four competing slot machines (‘four armed bandit’) with fluctuating, uncertain, outcomes (i.e. rewards and/or punishments, or neither). Decisions were made during periods of safety and environmental stress (threat of unpredictable shock). We predicted that anxious individuals under stress would learn faster about punishments, and exhibit choices that were more affected by them. We formalized these hypotheses in terms of parameter values – punishment learning rate and punishment sensitivity respectively - in reinforcement learning accounts of behaviour. We found no evidence for an effect on punishment choice sensitivity in the pathological group, even under elevated stress. However individuals with high anxiety symptoms did have higher learning rates for punishment across all conditions. The behaviour of the pathological group was also apparently more random, with a greater influence of a lapse parameter in the model across conditions. Overall, these data suggest that anxious individuals do not weigh negative outcomes more heavily; rather they are quicker to update their behaviour in response to negative (but not positive) outcomes. This suggests that, when treating anxiety, we should not seek to blunt responses to negative outcomes, but instead encourage anxious individuals to integrate information over longer horizons when bad things happen. As such, these findings provide a formal mathematical framework for developing psychological treatment strategies for mood and anxiety disorders.