I want to implement (discrete time, discrete state) dynamic programming in Matlab for my diploma thesis. I am not sure how to deal with the artificial upper and lower boundaries. Can someone propose me hints how to implement lower and upper boundaries in dynamic programming in general? The lower boundary is not so difficult as I would implement a CPPI rule to fully invest in the riskless asset when crossing the boundary. But how can I implement an artifical upper boundary condition that does not falsify the results in the recursive programming? Using the indirect utility from the previous period in t+1 will falsify the result because one neglects the possible upmoves that are not allowed. I thought about having a buffer of higher values with which I could calculate the indirect utilities but going back in time will still be problematic because the calculated indirect utilities become to small.Thanks

I have two ways to solve the problem:1. Augment the upper boundaries in such a way that the disturbances do not falsify the regions I am intersted in2. Keep a buffer of probabilities to cross the boundaries and extrapolate the indirect utilities beyond the boundaries.Is there any other (more elegant) way to deal with the boundaries?ThanksKai