# Tag Info

Accepted

### In Blackwell's condition for T to be a contraction mapping, we require that satisfies discounting. What is the intuition of discounting?

Without discounting, you cannot show either $$T(g + || f - g||) \leq Tg + \beta || f - g||$$ or $$T(f + || g - f||) \leq Tf + \beta || g - f||$$ and thus you cannot demonstrate that $T$ is ...
• 1,249
Accepted

### A Cake Eating Problem in Continuous Time: Hamiltonian or HJB?

The comment by user @MaartenPunt is accurate. I don't think that in general one can identify situations where one should have a clear preference over one formulation over the other. It is more of a ...
• 33.9k
Accepted

### Optimal stopping (reference request)

This is known as the McCall search model in economics. The original paper shows that the optimal stopping strategy rule is given by a "reservation wage", there is a threshold such that it is ...
• 13.5k
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• 1,924

### The Principle of Optimality and the Bellman Equation

Recall that the Principle of Optimality states that the solution to Our Bellman Functional Equation is the same as the solution to the sequential problem if: Assumption 1: $\Gamma(x)$ (our set of ...
• 8,487

### Has mathematical economics contributed to the mathematics of space exploration?

In the history of dynamic programming some economic works are considered pioneering contributions to the theory of dynamic programming (and in this sense it can be said that they contributed to ...
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• 638

### Bellman equation for this dynamic programming problem

The "second" constraint appears redundant and it confuses matters. Re-arrange the first one to obtain $$\tilde{a}_{t+1} = \big[\tilde a_t+(1-\delta )Y_t-\tilde{c}_t\big]R_t$$ This tells us that ...
• 33.9k
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• 661

### Capital accumulation

$a=0$ means implies the household does not enjoy leisure. In other words, the trade-off between consumption and leisure is switched off. It's not generally true that with $a=0$, utility is higher for ...
• 1,325

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

(This perhaps should be considered a comment.) If you have solved the HJB equation, it is sufficient to get the optimal solution. So you do not "have to be concerned with any other optimality ...
• 9,907
Accepted

### Why do game theorists use a discounted payoff of this form?

In my experience, it's mainly just for cleanliness for results. Consider an infinite horizon repeated game, with discounted payoff representation (where I use $\delta = (1-\lambda)$ in your notation)...
• 1,924

### What is state space representation for DSGE modeling

State Space Representations of Linear Systems: https://lpsa.swarthmore.edu/Representations/SysRepSS.html As systems become more complex, representing them with differential equations or transfer ...
• 780

### Solving a HJB with a probability to transit to a new state

I would leave this as a comment but I cant. You are on the right track. Once you know $V_2(k)$ then you can plug that into to the first hjb and solve. To solve for $V_2$ you need to find the optimal ...
• 151