Dear Mathematica users,
I'm trying to compute higher order derivatives of a moment generating function and then evalutate them in 0 (in order to get some moment conditions for a GMM estimation). Although I try to declare constants at the beginning of my script, which follows:
% Declaring constants
Constants -> {kappa, theta, sigma, gamma, b, dt, Uy, J, phi, lambda}
%
A[Uv_] = (-(kappa *theta)/(sigma^2))*((gamma + b)*dt +
2*Log[1 - ((gamma + b + (sigma^(2))*Uv)/(2*gamma))*(1 -
exp[-gamma*dt])]) + (exp[Uy*J] - 1 - Uy*phi*J)*lambda*dt;
%
B[Uv_] = -(a*(1 - exp[-gamma*dt]) -
Uv*(2*gamma - (gamma - b)*(1 - exp[-gamma*dt])))/(2*
gamma - (gamma + b)*(1 - exp[-gamma*dt]) -
Uv*(sigma^(2))*(1 - exp[-gamma*dt]));
% My moment generating function
EVPsi[Uv_] = exp[A[Uv]]*(1 - B[Uv]/omega)^(-v)
My problem is due to the fact that when I compute the first order derivative by using
EVPsi'[Uv] /. Uv -> 0
I get the following expression
% First derivative of the mgf evalueated in Uv=0
-v (1 + (a (1 - exp[-dt gamma]))/(
omega (2 gamma - (b + gamma) (1 - exp[-dt gamma]))))^(-1 -
v) (-((2 gamma - (-b + gamma) (1 - exp[-dt gamma]))/(
omega (2 gamma - (b + gamma) (1 - exp[-dt gamma])))) + (
a sigma^2 (1 - exp[-dt gamma])^2)/(
omega (2 gamma - (b + gamma) (1 - exp[-dt gamma]))^2)) exp[
dt lambda (-1 - J phi Uy + exp[J Uy]) - (
kappa theta (dt (b + gamma) +
2 Log[1 - ((b + gamma) (1 - exp[-dt gamma]))/(2 gamma)]))/
sigma^2] + (
kappa theta (1 + (a (1 - exp[-dt gamma]))/(
omega (2 gamma - (b + gamma) (1 - exp[-dt gamma]))))^-v (1 -
exp[-dt gamma]) Derivative[1][exp][
dt lambda (-1 - J phi Uy + exp[J Uy]) - (
kappa theta (dt (b + gamma) +
2 Log[1 - ((b + gamma) (1 - exp[-dt gamma]))/(2 gamma)]))/
sigma^2])/(
gamma (1 - ((b + gamma) (1 - exp[-dt gamma]))/(2 gamma)))
What I'm missing here is why I get in the last lines an expression such as
Derivative[1][exp][product of constants!!]
instead of a 0.
I would be thankful if you could shed some light on this. Thank you.
Exp
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