Before revision:  The value functionapproximations induced by Taylor polynomial expansions of the cost function prove however to converge only for entire cost functions with low growth orders , and to diverge otherwise.
After revision:  We review various cost approximation schemes and assess the convergence of the interval bounds these induce on the value function. Namely: Taylor expansions (divergent, except for a narrow class of entire functions with low growth orders , and to diverge otherwise.