Monotone strong increases in risk and their comparative statics

Abstract

We introduce a new concept of the monotone strong increase in risk (MSIR) order that imposes monotonicity restrictions on the ratio of the two cumulative of cumulative distribution functions as a special case of Rothschild–Stiglitz increases in risk that is the subset of the second-degree stochastic dominance criterion. We show that the MSIR order implies that the conditional expectation of a random variable under one cumulative distribution function is greater than or equal to that under another cumulative distribution function. Restricting the payoff function to be linear in the random variable and limiting our analysis to risk-averse decision-makers who are prudent, we obtain appealing comparative statics results for the MSIR shift. This general conclusion can be applied to prevailing economic models having a linear payoff.