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exp(-V(+1)/chi)/E_t[exp(-V(+1)/chi)]
again has the expectations around both expressions and is identical to 1.
You are not using a nonlinear transformation of the expectations themselves.
exp(-V(+1)/chi)/E_t[exp(-V(+1)/chi)]
EV = -(V(+1)/chi);
exp((-V(+1)/chi)-EV);
(1 + (1/1)*(-V(+1)/chi-EV) + (1/2)*(-V(+1)/chi-EV)^2 + (1/6)*(-V(+1)/chi-EV)^3)
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