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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 ...
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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 ...
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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 ...
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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 ...
...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 ...