stochastic dynamic programming - how to set up bellman and find FOCs
$begingroup$
I have a function:
$$ U = mathbb{E} bigg[ sum_{t=0}^{infty} beta^t ln c_t bigg]$$
Where $0<beta<1$ and my constraints are:
$$c_t + k_{t+1} = phi_t Ak_t^{alpha}, 0<alpha<1, k_1 = b_1 in mathbb{R}$$
where $phi_t$ is iid.
Then am I going about the correct way to find the FOCs?
Setting up the bellman we have:
$$ V_t(k_t) = max_{k_t}big{ln (phi_t AK_t^alpha -k_{t+1}) + beta V_{t+1}(k_{t+1}) big}$$
Am I on the right track?
stochastic-calculus dynamic-programming
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
$endgroup$
add a comment |
$begingroup$
I have a function:
$$ U = mathbb{E} bigg[ sum_{t=0}^{infty} beta^t ln c_t bigg]$$
Where $0<beta<1$ and my constraints are:
$$c_t + k_{t+1} = phi_t Ak_t^{alpha}, 0<alpha<1, k_1 = b_1 in mathbb{R}$$
where $phi_t$ is iid.
Then am I going about the correct way to find the FOCs?
Setting up the bellman we have:
$$ V_t(k_t) = max_{k_t}big{ln (phi_t AK_t^alpha -k_{t+1}) + beta V_{t+1}(k_{t+1}) big}$$
Am I on the right track?
stochastic-calculus dynamic-programming
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
$endgroup$
add a comment |
$begingroup$
I have a function:
$$ U = mathbb{E} bigg[ sum_{t=0}^{infty} beta^t ln c_t bigg]$$
Where $0<beta<1$ and my constraints are:
$$c_t + k_{t+1} = phi_t Ak_t^{alpha}, 0<alpha<1, k_1 = b_1 in mathbb{R}$$
where $phi_t$ is iid.
Then am I going about the correct way to find the FOCs?
Setting up the bellman we have:
$$ V_t(k_t) = max_{k_t}big{ln (phi_t AK_t^alpha -k_{t+1}) + beta V_{t+1}(k_{t+1}) big}$$
Am I on the right track?
stochastic-calculus dynamic-programming
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
$endgroup$
I have a function:
$$ U = mathbb{E} bigg[ sum_{t=0}^{infty} beta^t ln c_t bigg]$$
Where $0<beta<1$ and my constraints are:
$$c_t + k_{t+1} = phi_t Ak_t^{alpha}, 0<alpha<1, k_1 = b_1 in mathbb{R}$$
where $phi_t$ is iid.
Then am I going about the correct way to find the FOCs?
Setting up the bellman we have:
$$ V_t(k_t) = max_{k_t}big{ln (phi_t AK_t^alpha -k_{t+1}) + beta V_{t+1}(k_{t+1}) big}$$
Am I on the right track?
stochastic-calculus dynamic-programming
stochastic-calculus dynamic-programming
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
asked Dec 4 '18 at 23:38
elbartoelbarto
1,550824
1,550824
add a comment |
add a comment |
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