  In this paper, we study the optimal multiple stopping problem under Knightian
uncertainty both under discrete-time case and continuous-time case. The
Knightian uncertainty is modeled by a single real-valued function g, which is
the generator of a kind of backward stochastic differential equations (BSDEs).
We show that the value function of the multiple stopping problem coincides with
the one corresponding to a new reward sequence or process. For the
discrete-time case, this problem can be solved by an induction method which is
a straightforward generalization of the single stopping theory. For the
continuous-time case, we furthermore need to establish the continuity of the
new reward family. This result can be applied to the pricing problem for swing
options in financial markets, which give the holder of this contract at least
two times rights to exercise it.
