Risk Effects on Optimal Decision Making – A Question of the Right Order

We study risk effects, including higher-order risk effects, on optimal decision making in the linear-payoff model. This model includes the standard portfolio problem, the coinsurance problem, the problem of output choice with a risky price or a risky cost, and the problem of hedging a risky return as special cases. We distinguish between risk taking and risk mitigation and between uncertainty over a benefit and uncertainty over a cost. We identify restrictions on preferences for clear-cut comparative static effects of Nth-degree risk increases. For an uncertain benefit, the decision maker compensates increased risk by lowering exposure to risk; for an uncertain cost, the behavioral response depends on the parity of the order of the risk change. This is because only even-order risk changes increase the riskiness of terminal wealth while odd-order risk changes reduce it. To resolve this discrepancy, we introduce a new class of stochastic dominance relations that is suitable for uncertainty over a cost.