Abstract: Let Z_i be i.i.d.,and ε_i be i.i.d.,Bernoulli variables independent of Z_i.Set T_o ≡z and T_n=ε_n(T_n-1-Z_n)for n≥1.Using Wiener-Hopf type equations,we give a new approch to find optimal stopping rules for stopping T_n-nC,Where C＞0.Special cases are nsidered in detail,some of them are difficult to treat by Ferguson’s method.