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I am working on a dynamic programming problem with dimension over 1000. In this past, there exist methods like Smolyak algorithm and Adaptive sparse grid method to solve dynamic programming problem with dimension no more than 100. My question is does there exist an algorithm that that can deal with this. It is possible to reduce the dimension of my problem a little bit, but I am afraid it will lose some intuition.

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    $\begingroup$ could you be more specific ? $\endgroup$ Commented May 17, 2016 at 9:20
  • $\begingroup$ I would guess it is solvable only if there is some very special structure, otherwise hopeless... $\endgroup$ Commented May 17, 2016 at 12:09
  • $\begingroup$ What I am considering is a OLG model and I keep adding heterogeneity into OLG model. Those heterogeneity makes approximation equilibrium impossible. $\endgroup$ Commented May 17, 2016 at 13:37
  • $\begingroup$ If we assume there is no shock to depreciation rate but shock to TFP, then it may be possible to obtain some approximation results but it will lose some intuition. $\endgroup$ Commented May 17, 2016 at 13:39
  • $\begingroup$ in order to have a dimension reduction, could you specify the problem in very specific terms ? I mean, could you rephrase your problem into something like "I want to minimise xxx over yyy, dynamics is given by zzz model and so on.." $\endgroup$ Commented May 18, 2016 at 9:11

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