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• Thread: 62 Goods vs 13 No Goods

1. Economist
   c8f2
   

   I think one computational advantage in continuous time is that you lose the today/tomorrow distinction, and thus you roughly speaking remove one variable and achieve sparsity.
   What is less clear to me is how stochastic shocks, which are necessarily discrete are integrated in the framework. One can use jump processes I suppose but then some of the elegance seems to be lost.

   It seems possible that the linked paper is only "fast" because the author has only two shocks then. Otherwise I guess you don't get sparsity?

   As a non-numerical specialist I'm just surprised that this hasn't all been done though, in some sense. I thought that someone would have compared the PDE stuff against the best discrete-time stuff (I thought this was the point of Moll et al), but then, the above paper was just published last month.

   2 months ago # QUOTE 0 Volod 0 Vlad !

2. Economist
   627e
   

   Moll is a snakesoil salesman.

   But from the look of this threadz you're all so low IQ I'm not surprised you just go along.

   2 months ago # QUOTE 1 Volod 0 Vlad !

3. Economist
   c8f2
   

   Moll is a snakesoil salesman.
   But from the look of this threadz you're all so low IQ I'm not surprised you just go along.

   Uh ok. But can you clarify? Do you think the Rendahl paper shows the gains from cts time are illusory? And if you think Moll is a snake oil salesman, who or what do you suggest to guide practitioners on cts versus discrete-time?

   2 months ago # QUOTE 0 Volod 0 Vlad !

4. Economist
   787e
   

   Continuous time is very useful when:
   -You have multiple events that would be simultaneously happening in discrete time.
   -When computing transitions.
   -When you want elegant closed-form solutions.

   Otherwise, discrete time is just as good.

   2 months ago # QUOTE 0 Volod 0 Vlad !

5. Economist
   8691
   

   Continuous time is very useful when:
   -You have multiple events that would be simultaneously happening in discrete time.
   -When computing transitions.
   -When you want elegant closed-form solutions.
   Otherwise, discrete time is just as good.

   Discrete time is, and always will be, an approximation at best.

   2 months ago # QUOTE 0 Volod 1 Vlad !

6. Economist
   c8f2
   

   Continuous time is very useful when:
   -You have multiple events that would be simultaneously happening in discrete time.
   -When computing transitions.
   -When you want elegant closed-form solutions.
   Otherwise, discrete time is just as good.

   Ok but are there papers out there that give clearer guidelines, like, e.g., if you have an Aiyagari- problem with X state variables, grid size Y, and possible non-concavities, etc, then the optimal cts-time method takes [blank] time and the optimal discrete-time takes [blank] time (with the same tolerance between updates)?

   Or is this too much to ask for?

   2 months ago # QUOTE 0 Volod 0 Vlad !

7. Economist
   787e
   

   Continuous time is very useful when:
   -You have multiple events that would be simultaneously happening in discrete time.
   -When computing transitions.
   -When you want elegant closed-form solutions.
   Otherwise, discrete time is just as good.

   Ok but are there papers out there that give clearer guidelines, like, e.g., if you have an Aiyagari- problem with X state variables, grid size Y, and possible non-concavities, etc, then the optimal cts-time method takes [blank] time and the optimal discrete-time takes [blank] time (with the same tolerance between updates)?
   Or is this too much to ask for?

   It is too much to ask for, since the performance depends on how well you code the competing algorithms, the language, hardware, and so many extra assumptions (fineness of the grid, how you update guesses, ...)

   2 months ago # QUOTE 0 Volod 0 Vlad !

8. Economist
   c8f2
   

   Continuous time is very useful when:
   -You have multiple events that would be simultaneously happening in discrete time.
   -When computing transitions.
   -When you want elegant closed-form solutions.
   Otherwise, discrete time is just as good.

   Ok but are there papers out there that give clearer guidelines, like, e.g., if you have an Aiyagari- problem with X state variables, grid size Y, and possible non-concavities, etc, then the optimal cts-time method takes [blank] time and the optimal discrete-time takes [blank] time (with the same tolerance between updates)?
   Or is this too much to ask for?

   It is too much to ask for, since the performance depends on how well you code the competing algorithms, the language, hardware, and so many extra assumptions (fineness of the grid, how you update guesses, ...)

   But surely the numerical guys can give *some* sort of guidance? Otherwise, why all of the effort put in by Moll et al? e.g. use the same grid size, hardware, language, and focus on Aiyagari problems (with some bells and whistles, like adjustment costs or lifecycle concerns), and then run the PDE stuff against the usual discrete-time algorithms.

   Is it really true that no-one has done this systematically? The above Rendahl paper seems to do it for one two-state process and it seems he thinks cts-time doesn't add much.

   2 months ago # QUOTE 3 Volod 0 Vlad !

9. Economist
   2508
   

   To be clear, my point is that HJBs and viscosity solutions are understood when studying PDEs and optimal control problems, and you need little to no stochastic calculus to do this.

   These topics go hand in hand.

   2 months ago # QUOTE 0 Volod 0 Vlad !

10. Economist
    c8f2
    

    To be clear, my point is that HJBs and viscosity solutions are understood when studying PDEs and optimal control problems, and you need little to no stochastic calculus to do this.

    These topics go hand in hand.

    Yes but why should the practitioner care about the cts-time stuff? The key question should be very it is faster and/or more reliable than discrete-time, and as the above Rendahl paper illustrates, it isn't clear if this is true.

    2 months ago # QUOTE 3 Volod 0 Vlad !

11. Economist
    8988
    

    Continuous time is very useful when:
    -You have multiple events that would be simultaneously happening in discrete time.
    -When computing transitions.
    -When you want elegant closed-form solutions.
    Otherwise, discrete time is just as good.

    Discrete time is, and always will be, an approximation at best.

    This is a very silly point. You're writing down a model characterized by a handful of equations. Discrete time being an approximation is the least of your worries.

    2 months ago # QUOTE 4 Volod 0 Vlad !

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