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• 1,652
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What is the difference between comma and plus in the bellman equation?

You should be careful about the way you wrote your two equations because the $\max$ operators are different. In the first equation, you maximize an objective function on a set, meaning you look for ...
• 887
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What is unknown in Bellman Equation?

The original problem was probably of the form $$\max_{\{W_t\}_{t=1}^\infty}\sum_{t=0}^\infty \beta^t u(W_t-W_{t+1}),$$ $$\mbox{s.t. } W_{t+1}\in[0,W_t] \ \forall \ t, ~~ W_0 \mbox{ given}$$ When ...
• 4,188
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Bellman Equation with Two Discount Factors

No. Consider the following problem: Each period, one total unit of consumption falls from the sky that can be distributed between the two agents in any way. Their per-period utility is simply how much ...
• 13.4k
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Bellman equation corresponding to stochastic EZW recursive utility

What you have there are the preferences under an arbitrary policy -- what some call the prevalue function. The only thing missing is the max operator. Written with maximization (and making the state ...
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What is the result of the Bellman Equation

...the result of applying sup operator is a NUMBER... Read it carefully. The equation is $$v(x_0) = \sup_{ \{x_t \}_{t \geq 1}} \cdots \quad (1)$$ This defines a function $v$, called the value ...
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• 661
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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
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Wealth in the utility function

Two points: As Richard Hardy points out in the comment, there is not really any depiction of wealth in the question. I am very curious which model this is. I can not think of any models that include ...
• 721
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• 2,619
1 vote

What is unknown in Bellman Equation?

What you want to maximize is the discounted stream of utility over time. To that end, you can set control variables over time (subject to some constraints, like technology, budget...). We are ...
1 vote
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Solution to the Bellman equation is a fixed point

I am by no means an expert on this, but maybe this helps. Here is a simple example for a bellman equation $V(y) = \max_x u(x,y) + \beta V(y')$ $s.t. \, y' = f(x,y)$ This is a functional equation in ...
• 970

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