A brief note on the soundness of Bermudan option pricing via cubature
  The subject of this study is an iterative Bermudan option pricing algorithm based on (high-dimensional) cubature. We show that the sequence of Bermudan prices (as functions of the underlying assets' logarithmic start prices) resulting from the iteration is bounded and increases monotonely to the approximate perpetual Bermudan option price; the convergence is linear in the supremum norm with the discount factor being the convergence factor. Furthermore, we prove a characterisation of this approximated perpetual Bermudan price as the smallest fixed point of the iteration procedure. 
Frederik S. Herzberg