  In this paper we consider the Parisian ruin probabilities for the dual risk
model in a discrete-time setting. By exploiting the strong Markov property of
the risk process we derive a recursive expression for the fnite-time Parisian
ruin probability, in terms of classic discrete-time dual ruin probabilities.
Moreover, we obtain an explicit expression for the corresponding infnite-time
Parisian ruin probability as a limiting case. In order to obtain more analytic
results, we employ a conditioning argument and derive a new expression for the
classic infinite-time ruin probability in the dual risk model and hence, an
alternative form of the infnite-time Parisian ruin probability. Finally, we
explore some interesting special cases, including the Binomial/Geometric model,
and obtain a simple expression for the Parisian ruin probability of the
Gambler's ruin problem.
