Portfolio Dominance and Demand for Risky Assets under Risk Taking Behavior

An important question under uncertainty concerning the economic environment is how the change in distribution of the random variable affects the optimal level of the decision variable chosen by a decision maker. This paper proposes two types of portfolio dominance orders for the standard portfolio model, a ‘strong portfolio dominance’ (SPD) and a ‘relatively strong portfolio dominance’ (RSPD). The difference between these two concepts is the number of crossing times of two PDFs for the left‐side of the point r. While two probability density functions (PDFs) cross only once in the case of the SPD order, the RSPD order allows two PDFs to cross many times. The relationship between them shows that the SPD shift is a subset of the RSPD one. The comparative statics results for these two shifts imply that there is a trade‐off between the restrictions on the set of changes in cumulative distribution function (CDF) (or PDF) and the set of the decision makers expressed as the shape of utility function. That is, compared with the result for the SPD order, the comparative statics result for the RSPD one includes a larger set of FSD changes and a smaller set of the decision makers.