hey folks,i have to solve a dynamic model with a nonstandard return(reward) function, which is not differentiable in exogenous state variable s and not continuous in policy function x', i.e. i have the following:v(s,x) = max_{x} {f(s, x, x') + beta*E[v(s', x')|s,x]}where s is a 2-D exogenous state variable and x is a 2-D endogenous state variable. prime denotes the next period value but not derivative. Note that the return function f(s, x, x') is not differentiable in s.I know the standard discretized state space method works when a coarse grid is used, while method suffers from the curse of dimensionality when the grid gets finer. Due to the discontinuity/nondifferentiability, the projection (collocation) method does not work out. Would you guys have any suggestions?cheers

no solution after more than 600 views? physicists, mathematicians, please shout out!

Are you working on the commercial or academic side of things? If the latter, you could run on teragrid and see if massive parallelism is the way to go. However excessive queue times might make this impractical in reality, and teragrid is a little shaky Alternatively, what about some kind of adaptive step size control, eg., there's a paper by Hoffman et al

I think you mentioned you're in academia before we lost Friday's posts, so here's the paper reference which your institution should have access to.

i just download the paper from jstor. it seems very sexy. thanks a lot.