  In this paper, we study the optimal multiple stopping problem under the
filtration consistent nonlinear expectations. The reward is given by a set of
random variables satisfying some appropriate assumptions rather than an RCLL
process. We first construct the optimal stopping time for the single stopping
problem, which is no longer given by the first hitting time of processes. We
then prove by induction that the value function of the multiple stopping
problem can be interpreted as the one for the single stopping problem
associated with a new reward family, which allows us to construct the optimal
multiple stopping times. If the reward family satisfies some strong regularity
conditions, we show that the reward family and the value functions can be
aggregated by some progressive processes. Hence, the optimal stopping times can
be represented as hitting times.
