The name is absent

MS function is restricted by Proposition 2. For example, Properties 1 and 2 make it
monotonously increasing in μ and decreasing in σ, respectively. Property 4 stipulates that
the relevant Hessian matrix with respect to μ and σ is negative semi definitive. Properties 5
and 6 restrict the slope of the indifference curve when the individual is risk averter. Property
5 makes S(σ,μ) to be decreasing (constant, increasing) in μ when the individual’s absolute
risk aversion is decreasing (constant, increasing), while Property 6 makes it to be decreasing
(constant, increasing) along rays through the origin when the individual’s relative risk
aversion is decreasing (constant, increasing).³ For later convenience, they are summarized as
follows (This study focuses on risk averter’s case).

⁽¹⁾                                          Vμ (^σ, μ )> 0^,

(2)                                        V ( σ, μ )< 0 ,

(³-ⁱ)                                           Vμμ (^σ, μ)≤ ^{0 ,}

(^3-ii)                                          Vσσ (^σ, μ)≤ ^{0 ,}

(^3-iii)                            Vμμ (^σ, μ) Vσσ ^(σ, P^{)- V}2 ^(σ, P)≥ ^{0 ,}

(^4-i: DARA)           ^-Vμσ (^σ, μ) Vμ (^σ, μ) + Vμμ (^σ, μ) ∖' (^σ, μ) < 0 ^,

(4-ii: CARA)          -V_μσ (σ, μ)V_μ (σ, μ) +V_μμ (σ, μ)V_σ (σ, μ) =0,

(4-iii: IARA)           -V_μσ (σ, μ)V_μ (σ, μ) +V_μμ (σ, μ)V_σ (σ, μ) >0,

(5-i: DRRA)

{-V_μσ(σ,μ)V_μ(σ,μ)+V_μμ(σ,μ)V_σ(σ,μ)}μ+{-V_σσ(σ,μ)V_μ(σ,μ)+V_μσ(σ,μ)V_σ(σ,μ)}σ<0,

(5-ii: CRRA)

{-V_μσ(σ,μ)V_μ(σ,μ)+V_μμ(σ,μ)V_σ(σ,μ)}μ+{-V_σσ(σ,μ)V_μ(σ,μ)+V_μσ(σ,μ)V_σ(σ,μ)}σ=0,

(5-iii: IRRA)

{-V_μσ(σ,μ)V_μ(σ,μ)+V_μμ(σ,μ)V_σ(σ,μ)}μ+{-V_σσ(σ,μ)V_μ(σ,μ)+V_μσ(σ,μ)V_σ(σ,μ)}σ>0.

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