“…For these reasons, a theory has been developed in [7,8,5] that gives precise bounds on asymptotic performance for schemes that are based on subsolutions to this HJB equation rather than to the solution itself; see also [3] for the closely related concept of the associated Lyapunov inequalities, that can be also used to find bounds of the performance measures in the prelimit. Such results have been used to test the efficiency of state-dependent importance sampling schemes in the heavy tail and discrete setting, e.g., [1,2,4,8].…”