Heterogeneity of Investors and Asset Pricing in a Risk-Value World

It remains to be shown for 7 < 1 that g⅛_ε → 1 for ε → ∞. For ε → ∞,
e_iε → ∞ for at least one investor. By equation (43), e_iε → ∞ if π_ε— 1+s_i → 0.
Since π_ε — 1 + s_i > 0 Vi, ε and s⅛ < Sj Vj, j = h,π_ε — 1 + s_i → 0 for ε → ∞
must hold for i = h only. Hence e_hε → ∞ and, therefore, by equation (44),
gh_ε → 1 for ε → ∞. It follows from π_ε — 1 + s⅛ → 0 for ε → ∞ and π_ε > 0
that Sf_l must not exceed 1.                                                ■

46

<<   43   44   45   46   47   48   49   >>

More intriguing information