# Questions tagged [dynamic-optimization]

The tag has no usage guidance.

70 questions
Filter by
Sorted by
Tagged with
1 vote
26 views

### Utility maximization across yield curves?

I'm attempting to solve a utility maximization problem for return-on-investment (ROI) across two different products, where each product experiences a different linear ROI curve. For product one, the ...
• 11
40 views

### Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris

The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
56 views

### Current best methods for solving dynamic optimization problems in high dimensional state spaces

I was wondering what the current best methods are for solving dynamic optimization problems in high dimensional state spaces. Let me lay out the common cases where I would do something like this in ...
• 355
31 views

### dynamic macroeconomics: Does the system "state" affect the dynamic optimization problem?

I am new to economics, but come from a statistics and math background, so the control theory and dynamic optimization ideas are familiar to me. What is a little confusing is that in most control ...
• 355
40 views

### What assumptions can be made to ensure convexity in this optimization problem?

This question is a continuation of the question I asked at: How can I show convexity of this value function? Where I came to the conclusion that more assumptions are required to show that the ...
• 183
210 views

### How can I show convexity of this value function?

I have set up an optmization problem as follows: $$V(A)=\max_{l, C} \quad u(C,l)$$ Where the only constraint is as follows: $$C=f(l,A)$$ Here $u$ is the utility function which captures social welfare. ...
• 183
169 views

### How can I formulate the following optimization problem?

I want to set up an optmiization problem for global warming in which a planner determines how much carbon dioxide gas is emitted. Let's say we reduce this problem down to two periods, then I ... 85 views

### What is the 'fixed point problem'?

I understand what the fixed point is, but don't understand what the fixed point 'problem'. Is it resolved by 'fixed point iteration'? I am reading a paper, and the paper mentions that the default ...
48 views

### Necessary conditions in overlapping generations model (OLG)

The consumer at each period maximizes \begin{equation} \displaystyle\sum_{i=1}^{I}\beta^{i-1}U(c^i_{t+i},l^i_{t+i}) , t=0,1,2,3,... \end{equation} subject to \begin{equation} (1+\eta_t)c^{i}_t+...
36 views

### 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 ...
• 21
47 views

• 2,239
38 views

### Value function iteration with stochastic productivity's standard deviation

Hello I would like to know how would you discretize the AR(1) process of technology in a standart RBC model when there is stochastic productivity's standard deviation. Namely I have: Technology $Z_t$ ...
• 437
48 views

• 717
65 views

### Neoclassical Two-Sector Model of Endogenous Growth: Getting the consumption growth rate

I'm struggling to derive the growth of consumption from a two-sector model with the traditional Cobb-Douglas function. The model I am speaking about incorporates the fractions used by physical and ...
1 vote
90 views

### reference request - dynamic discrete time optimization methods

Next semester I am taking business cycle theory course. I emailed my teacher and he replied that I need firm understanding of dynamic discrete time optimization methods. I am gonna study mainly from ...
• 113
35 views

### Resolution - Ramsey growth model with per capita variables

Let's say that we have the sum of the utility of a social planner $$\int_{0}^{\infty}U\left(C\right)e^{-\rho t}dt$$ where $C$ is the total consumption. If we want to write this by a per capita ...
• 2,095
1 vote
112 views

### Introduction of an asset tax in the AK model

Let's start by analyzing the family's problem with the imposition of a tax. Assuming a CRRA utility function: \begin{equation} U = \int_0^\infty e^{-(\rho-n)t} \cdot \left[ \frac{c^{1-\theta}-1}{1-...
• 390
107 views

### 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: $x(t)$: ...
• 717
58 views

### 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 ...
• 87
1 vote
138 views

### Solving a HJB with additional constraints on control and state variables

I am trying to solve a Hamiltonian-Jacobi-Bellman equation with additional constraints on the state and control variables, but I am a bit confused on how to do that. In Intrilligator 2002, it is ...
• 41
60 views

### How to optimize this dynamical system? Needing guidelines

I'm trying to solve a growth model, where the author indicates is a dynamical system. I want to ask if someone would help me with some guidelines of how to optimize this, I've been trying to solve it ...
• 31