Changes in Risky Benefits and in Risky Costs: A Question of the Right Order

We organize and extend findings on the comparative static effects of risk changes on optimal behavior in a unifying expected utility model. We determine restrictions on preferences for clear-cut results. Risk increases of a benefit are compensated by lowering exposure to risk. For risk increases of a cost, the response depends on the order of the risk change. This discrepancy arises because even-order risk increases of a cost raise the riskiness of the payoff distribution, whereas odd-order risk increases of a cost reduce it. We identify the stochastic dominance orders to resolve this discrepancy and discuss specific decision problems as applications.