restricted as well. Compared with the case mentioned above, solving this specification
problem is however somewhat complicated, because the LS condition does not specify a
distribution of random payoffs but forms such a distribution family that nests a number of
distribution, e.g. normal distribution and uniform distribution. Picking up a particular
distribution from the LS distribution family loses generality of the condition. Therefore, the
MS function under LS condition needs to be specified directly from MS framework, meeting
the conditions that are imposed on MS function under the LS condition. Several attempts
such as studies by Saha (1997) and Eggert and Tveteras (2004) were made to directly specify
the MS function under the LS condition. However, nobody has pointed so far that the
conditions have not been sufficiently fulfilled and that the conditions themselves have not
been thoroughly discussed.
The objective of this study is to examine the functional specification of MS approach
under the LS condition. The specification procedure adopted here is the one which directly
specifies the MS function so that it fully meets the conditions imposed under the LS
condition. Although the direct specification procedure relies upon a trial-and-error method
that is far from mathematical elegance, it is suitable for exploring the possibility of
specifying the MS function under LS condition. This study proceeds in the following order.
Firstly, preliminary discussion is made on the conditions imposed on MS function under the
LS condition. The conditions come from three sources, which are (a) cardinal property of
vNM utility function, (b) behavioral hypotheses that are translated from EU theory into MS
approach, and (c) relationship between Arrow-Pratt's risk aversion measures. Then, the
imposed conditions are categorized by the type of risk aversion measures. Secondly, the
direct specifications of MS function are applied to each type of risk aversion. In particular, it
is examined whether the two functional properties, additive separablility and homotheticity,
are applicable to the functional specifications. Based on the examinations, MS functions
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