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We consider the optimal stopping of independent, discrete time sequences X 1 , . . . , X n where m stops are allowed. The payoff is the sum of the stopped values. Under the assumption of convergence of related imbedded point processes to a Poisson process in the plane we derive approximatively optimal stopping times and stopping values. The solutions are obtained via a system of m differential equations of first order. As application we consider the case that in the domain of attraction of andoi:10.1137/s0040585x97986011 fatcat:ermuadfmzzefroy5ki4jkw6tmq