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.