  In a general Feller martingale market with several assets, the existence of
optimal exercise regions for multi-dimensional Bermudan options can be
established by reference to Neveu's theory of Snell envelopes -- and also, as
will be shown, more directly from standard martingale arguments combined with
the strong Markov property. Based on this, in the framework of a log-L\'evy
martingale market, explicit formulae and asymptotic results on the perpetual
American-Bermudan (barrier-like) put option price difference (``continuity
correction'') near the exercise boundary will be proven, under the -- of
course, fairly restrictive -- assumption that the logarithmic optimal exercise
region, subject to the barrier, does not depend on the time mesh size and is,
up to translation, a half-space.
  For this sake, Wiener-Hopf type results by Feller will be generalized to
higher dimensions. It will be shown that an extrapolation from the exact
Bermudan prices to the American price cannot be polynomial in the exercise mesh
size in the setting of many common market models, and more specific bounds on
the natural scaling exponent of the non-polynomial extrapolation for a number
of (both one- and multi-dimensional) market models will be deduced.
