The Comparative Statics for Linear Payoffs and Increases in Risk

This paper introduces a concept for the subset of K-L-L-S increases in risk defined by Kroll, Leshno, Levy, and Spector (1995; called K-L-L-S); a ‘relatively strong increase in risk in the K-L–L-S sense’ (RSIRK). Our new notion of K-L-L-S increases in risk extends the Rothschild-Stiglitz definition of risk to a larger set of cumulative distribution functions, but use somewhat stronger restrictions on the structure of the decision model and the set of decision-makers. The decision model used in this paper consists of a utility function of one scalar variable that is affected by one-dimensional choice variable (and another random variable) to avoid problems involving multidimensionality. We show that, by restricting the payoff function to be linear in the random variable ( 0 = xx z ) and limiting our analysis to decisionmakers who are prudnet ( 0 ≥ ′ u ), we are able to generate comparative statics results for the RSIRK order.