Not fully agree. The notion of “stage” is more fundamental and intrinsic. The notion “node” embodies an implication/restriction—you are restricting the underlying true stochastic process to be a scenario tree.
Now I want to ask:
- is it possible to carry out a SDDP algorithm even if we do not pre-construct a finite scenario tree? (e.g. we only provide a sampler, will this be sufficient?)
One more question related: Markovian SDDP: is a finite and concrete scenario tree necessary?