Comparative statics tests between decision models under risk

We present several comparative statics theorems that distinguish between major decision models under risk. Our main interest is to sort out three models: expected utility (EU), expected utility with rank dependent probabilities (EURDP), and implicit weighted utility (IWU). To begin, we use the two asset portfolio problem to distinguish between EU and EURDP investors; specifically, we identify a change in the distribution of the risky asset such that all risk averse EU maximizers invest more in the risky asset, but some risk-averse EURDP maximizers invest less. We then develop tests between EURDP and IWU: all risk-averse EURDP maximizers increase a choice variable in response to a given change in the distribution of an exogenous variable, while some risk-averse IWU maximizers do not. We also use 'local' utility analysis to illustrate our procedure and to explain why the expected utility comparative statics that we use need not be preserved for 'smooth' non-expected utility representations.