<p>Its known that the Bellman equation in recursive macroeconomics is used for the following problems:</p>

<p><span class="math-container">$$\sum_{t=1}^\infty\beta^tU(c_t)$$</span>
<span class="math-container">$$s.t. c_t+k_{t+1}=f(k_t)$$</span>
<span class="math-container">$$k_0&gt;0$$</span></p>

<p>Im wondering if we can apply the bellman equation to problems with finite horizon. The reason why I ask is because it would be considerably easier solving a bellman for a policy function than to solve for these values sequentially.</p>

CC BY-SA 4.0
2019-11-18T22:01:33.163Z
I might not understand this question, but the answer seems to be trivially yes, since that's how (i.e. from finited time horizons) is how the Bellman equation is actually derived.  See 1.5 in https://www.ssc.wisc.edu/~nwilliam/Econ712/lect7.pdf
fantastic peace and prosperity
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2019-11-22T19:23:21.383Z
My recent answer to this question may be helpful: https://economics.stackexchange.com/questions/32711/dynamic-programming-optimal-consumption-savings-finite-horizon-problem/32867?noredirect=1#comment49850_32867
Walrasian Auctioneer
<bellman-equations><recursive-macroeconomics>
Can the Bellman Equation be used for Finite time problems?
EconJohn
# Can the Bellman Equation be used for Finite time problems?

(Asked by: username_0 on 2019-11-18)

Its known that the Bellman equation in recursive macroeconomics is used for the following problems:

$$\sum\_{t=1}^\infty\beta^tU(c\_t)$$
$$s.t. c\_t+k\_{t+1}=f(k\_t)$$
$$k\_0>0$$

Im wondering if we can apply the bellman equation to problems with finite horizon. The reason why I ask is because it would be considerably easier solving a bellman for a policy function than to solve for these values sequentially.

**Tags:** bellman-equations, recursive-macroeconomics

> **Comments:**
> **username_1**: I might not understand this question, but the answer seems to be trivially yes, since that's how (i.e. from finited time horizons) is how the Bellman equation is actually derived.  See 1.5 in https://www.ssc.wisc.edu/~nwilliam/Econ712/lect7.pdf  
> **username_2**: My recent answer to this question may be helpful: https://economics.stackexchange.com/questions/32711/dynamic-programming-optimal-consumption-savings-finite-horizon-problem/32867?noredirect=1#comment49850_32867  

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