Questions tagged [dynamic-programming]

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21
votes
3answers
692 views

When Optimal Control fails (?)

In order to "ask my question", I have to solve a model first. I will omit some steps but still, this will unavoidably make this post very long -so this is also a test to see whether this community ...
14
votes
1answer
2k views

Solving the Hamilton-Jacobi-Bellman equation; necessary and sufficient for optimality?

Consider the following differential equation \begin{align} \dot x(t)=f(x(t),u(t)) \end{align} where $x$ is the state and $u$ the control variable. The solution is given by \begin{align} x(t)=x_0 + \...
7
votes
3answers
752 views

Solution Method for Infinite-Horizon Maximization Problem

Full disclosure: this problem was part of a final exam that none of our class could really solve definitively. Below the general form is a specific utility function we worked with that I'll try to ...
6
votes
2answers
199 views

Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
3
votes
0answers
670 views

Market clearing condition with Walras law

I have a diamond overlapping model The question is as follows Let us consider an infinitely lived production economy populated at time t by $N_t$ identical and perfectly competitive adult ...
2
votes
2answers
253 views

Dynamic programming, optimal consumption-savings (finite horizon) problem

Let $w_t$ denote a consumer's wealth at time $t$ and $c_t$, the amount she chooses to consume, so her savings exiting this time period are $w_t-c_t$. Given this savings decision, her savings $w_{t+1}$ ...