The name is absent

Conditions (1), (2), (3-i), (3-ii) and (3-iii) are derived from Properties 1, 2 and 4, respectively,
and they are imposed at all times when individual is risk averse under LS condition.

Conditions (4-i), (4-ii) and (4-iii) could be expressed by Property 5 in terms of V (σ, μ).
Similarly, conditions (5-i), (5-ii) and (5-iii) could be expressed by Property 6 in terms of
V (σ, μ) when t = 1. They are depending on types of risk aversion.

Thirdly, as discussed by Saha (1997), Arrow-Pratt risk aversion measures impose a
certain restriction on the relationship between absolute risk aversion and relative risk
aversion. Formally, let A(π) and R(π)= πA(π) respectively denote absolute risk aversion
and relative risk aversion. Then the differentiation of R(π) yields R_π(π)=A(π)+πA_π(π). If
absolute risk aversion is decreasing (DARA), i.e., A(π) > 0 and A_π (π)< 0, then the sign of
R_π (π) is not determined. In other words, DARA does not restrict the type of relative risk
aversion. However, when absolute risk aversion measure is constant (CARA) or increasing
(IARA), i.e., when A(π) > 0 and A_π (π)≥ 0 , the sign of R_π (π) is restricted to be positive,
that is, increasing relative risk aversion (IRRA) is indicated and decreasing relative risk
aversion (DRRA) and CRRA are ruled out. As shown in table 1, the combination of absolute
and relative risk aversion is uniquely determined, except that relative risk aversion is not
restricted under DARA and absolute risk aversion is not restricted under IRRA. Under the
EU formulation, special attention needs not to be paid to the relationship, since it is
automatically fulfilled in the specification of vNM utility. For example, if vNM utility is
specified as a negative exponential function that indicates CARA, then IRRA automatically
follows. However, its fulfillment is not guaranteed in the MS approach. Therefore, the
relationship must be explicitly taken into consideration in the specification of the MS
function in order that the relationship is maintained. Specifically, as Properties 5 and 6 in
Proposition 2 implicitly assume the relationship, attention has to be paid to both of them.
This imposes another restriction on MS function. For example, if MS function displays

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