Optimal Policy with Low-Probability Extreme Events

The optimal policy response to a low-probability extreme event is examined. A simple policy problem is solved for a sequence of different loss functions: quadratic, combined quadratic/absolute-deviation, absolute-deviation, combined quadratic/constant, and perfectionist. The paper shows that, under some simplifying assumptions, each of these loss functions puts less weight on a low-probability extreme event than the previous one, down to the quadratic/constant and perfectionist loss functions, which completely ignores the low-probability extreme event. The case when the size of the extreme shock is endogenous and depends on the policy is also examined. This introduces an additional effect on the optimal policy except for the combined quadratic/constant and the perfectionist loss functions.