# Questions tagged [dynamic-programming]

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### What is the best way to learn applied dynamic programming?

I want to learn dynamic programming in a more applied fashion. I want to be able to solve problems of the likes of Recursive Macroeconomic Theory. I want to be able to solve problems using pen and ...
1 vote
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### Cake eating problem with income over time

I'm trying to implement a solution to a dynamic programmig exercise (cake eating) in Python. Consider the following problem. An individual lives for 20 periods. In the first 15 periods he receives an ...
1 vote
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### What exactly is an exogenous stationary distribution?

All jobs are identical except for their wages, and wages are given by an exogenous stationary distribution of $F (w )$ with finite (bounded) support $\mathbb W$. This is from page 6 of https://ocw....
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1 vote
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### How to solve dynamic problem with 2 production functions?

Suppose we have the following problem: $\max \int_0^\infty \exp(-\rho t) u(c(t))dt$ where $c(t)$ is consumption at time $t$. Subject to: $\dot{k}(t)= f(k(t))- c(t) - \delta k(t)$. where $k$ is capital,...
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### Has mathematical economics contributed to the mathematics of space exploration?

We see the work of Bellman showing up in both orbital trajectory planning/optimization and, obviously DSGE modeling. Also, in a recent example, the JWST uses ideas surrounding Pareto optimization and ...
1 vote
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### Does this contraction mapping map strictly concave functions into strictly concave functions?

Consider the following functional equation: $$TV(k)=\max[W(k),\beta V(f(k))]$$ where $\beta\in (0,1)$, $W(k)$ is continuous, increasing, bounded, and strictly concave function defined on $[0,\bar{k}]$,...
151 views

### How can I show that the policy function is non-decreasing?

Consider the following functional equation: $$V(x)=\max_{y\in [0,f(x)]}[u(f(x)-y)+\beta V(y)]$$ where $u$ is continuous, strictly increasing, and strictly concave; the function $f$ is continuous and ...
91 views

### Understanding Duality between Individual and Collective Maximization in Macroeconomic Models

I'm currently studying macroeconomic models, specifically from the book "Recursive Macroeconomic Theory." In Chapter Seven, it is mentioned that some economic models involving firms and ...
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### How can I show that the optimal savings are 0 for all time periods?

Consider an infinitely-lived agent’s consumption-saving problem. The agent receives $e > 0$ units of endowment every period, can save via an asset with constant return $R$. The agent is endowed ...
1 vote
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### Bellman Equation & Envelope Theorem

I'm unsure where the envelope theorem comes into play when i differentiate the Bellman Equation with respect to $k_t$. To me it looks like the regular chain rule and in fact the exact opposite of the ...
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### Simulation of a dynamic search and matching model

I want to simulate a search and matching model very close to the canonical model developed by Pissarides. I am interested in representing the trajectory of the unemployment rate when the unemployment ...
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### One shot-deviation property for games of imperfect information

The equivalence between subgame perfection and one-deviation property is typically stated for games of perfect information (where information sets are singletons). Does the Blackwell-style argument ...
156 views

### Mathematical Prerequisites for Recursive Macroeconomic Theory (Thomas J Sargent, Lars Ljungqvist)

I'm a math grad who is interested in learning more about economics for fun. Reading through RMT, I saw some interesting math (in chapter 2) around using "invariant functions" to determine ...
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1 vote
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### Are there any sophisticated'' mathematical modelling where they solve for the utility function?

Are there any references in literature of any sophisticated'' mathematical modelling where they solve for the utility function under specific conditions using differential equations theory? In such ...
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### When do Economists use the Linear Quadratic Regulator in simulating DSGE models

I was watching some excellent videos on DSGE models by Klaus Pretner. The author was able to solve some simple model such as the Ramsey-Cass-Koopman's model, and a New Keynesian model with frictions, ...
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### More equations than endogenous variables in RBC model

I recently came across my late father's bachelor's thesis, in which a RBC model is described. It appears to be a variant of Hansen's 1985 model with indivisible labor. I wrote the model into Dynare to ...
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1 vote
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### How to define a dynamic programming problem in an incomplete information game?

How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
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### What is state space representation for DSGE modeling

I'm beginning with DSGE modeling, and a mathematical representation (perhaps trivial for most of the people that are more with this topic) is the space-state state representation of a dynamical model, ...
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### Optimization in discrete time

I have made optimizations in continuous time that belong to the control theory, for example one case: $\max(\min)V[u(t)]=\int_0^Tf(t,x(t),u(t))dt$ constraint to: $\dot x=g(t,x(t),u(t))$ Where: $x(t)$: ...
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### Can anyone help me understand the Motrtensen-Pissarides model?

I am seeking help with the Mortensen-Pissarides model in discrete time? Basically, I was given the following in class example (which we didn’t complete do to time constraints associated with the end ...
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### Solving a HJB with a probability to transit to a new state

I am trying to solve the problem of a firm facing the possibility of a future tax, in continuous time. The firm maximizes $V(k)=\int_{t=0}^{\infty}e^{-rt} \pi_t dt$ with $\pi_t=f(k_t)-i_t$ and \$\dot{k}...
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