problem with dynamic optimization solution when increasing the scaling parameter value of the objective function

I am solving a very simple economic dynamic optimization model. First I have solved the model using discrete state and control spaces. In the model I have a utility function, and theoretically if I scale the utility function in a certain way the solution should be identical. Which is working for the code I am using to solve the model with discrete state and control spaces. But I am also solving the same model using continuous state and control spaces. To do that I wrote a code using a toolbox called CEtools. Now my problem is as I change the scaling of the utility function in the second code it only works up to a point. If I keep increasing the scaling parameter at some point the code breaks, that is it gives zero for the control value for any state value.

Did any one ever experienced a problem like this? Or may be anyone more experienced can suspect the problem I am missing here.

Thanks Dina

Answer 1

[Sargondjani]

What is your utility function and how do you scale it? And is zero also your starting value for the controls?

The only thing that comes up immidiately is that the scaling forces the gradient to something very small so fmincon thinks it has found an optimum (for instance if you have a CARA utility function -exp(-alpha*C)/alpha then for large values of consumption the derivative becomes very small).

I have no clue how cetools works, so could be something in there too. I am actually interested in your problem so you could send me a message that gets forwarded to my email, so we can discuss further there...