The name is absent

follows.

Proposition 4 (homotheticity and nonhomotheticity)

(1) If an individual is risk averter of DRRA under LS condition, then the MS function is
non-homothetic function whose expansion path is strictly concave in σ - μ axis.

(2) If an individual is risk averter of CRRA under LS condition, then the MS function is
homothetic.

(3) If an individual is risk averter that displays the combination of IRRA and DARA under
LS condition, then the MS function is non-homothetic function whose expansion path is
strictly convex in σ - μ axis.

A flexible specification

The specification of MS approach under LS condition has been considered for each type of
risk aversion and then several MS functions have been proposed (see forms (6), (9), (10) and
(12)). They can be applied to empirical analysis, assuming that the agent displays the
corresponding type of risk aversion and the random payoffs it faces are restricted to the
distribution class that satisfies the LS condition. However, as pointed out by Sinn (1983) and
Meyer (1987), a wide range of EU-based economic models satisfies the LS condition owing
to the theoretical structures themselves, and in such models, the EU theory is interchangeable
with MS approach with no assumption imposed on vNM utility function. Therefore, a
particular type of risk aversion needs not to be imposed a priori. In order to exploit the MS
approach in empirical studies based on the LS class of economic models, we need to specify
MS function flexible enough to nest as many types of risk aversion as possible. As far as the
author knows, Saha (1997) is the first who tackled this flexible specification problem of the
MS function. He proposed a nonlinear mean-standard deviation (NLMS) model,

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