Optimal multiple stopping with sum-payoff

We consider the optimal stopping of independent, discrete time sequences X1, . . . , Xn 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 Xi = ciZi + di with (Zi) i.i.d. in the domain of attraction of an extreme value distribution. We obtain explicit results for stopping values and approximative optimal stopping rules.