The name is absent

utility function and/or distribution of random payoff, EU theory derives a MS function such

function, F (π) is a cumulative distribution function of π, V (σ, μ) is the derived MS function
and μ and σ denote the mean and the standard deviation of π, respectively. A positive

linear transformation of the vNM utility function derives the relationship,

au(π) + b}dF(π) = aV(σ, μ) + b (a > 0), which indicates the following result.

Proposition 1 (Cardinal property)

If MS approach is explained within EU theory, then the MS function is also cardinal that is
transformable only by a positive linear function.

Secondly, Sinn (1983) and Meyer (1987) translated under LS condition the EU-based
behavioral hypothesis such as vNM utility’s curvature and Arrow-Pratt’s measures of risk
aversion into appropriates analogues of MS approach.

Proposition 2 (Behavioral hypothesis)

Property 1 V_μ (σ, μ) > 0 if and only if U_π (π)> 0.

Property 2 V_σ (σ, μ) < 0 ( = 0 ) if and only if U_ππ (π) < 0 ( = 0 )

Property 3 The slope of the indifference curve of V ( σ, μ ), denoted

as S (σ, μ) = -V_σ (σ, μ)∣V_μ (σ, μ), is positive (zero) if the agent is risk-averse (risk-neutral).

Property 4 V (σ, μ) is concave if and only if U_π (π) > 0 and U_ππ (π) ≤ 0 .

Property 5 S_μ (σ, μ) < 0 (= 0, > 0) if and only if absolute risk aversion is decreasing (constant,

increasing).

Property 6 S_t (tσ,tμ) < 0(=0,>0) if and only if relative risk aversion is decreasing (constant,
increasing).

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