Optimal Multiple Stopping with Sum-Payoff

A. Faller, L. Rüschendorf
2013 Theory of Probability and its Applications  
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 an
more » ... attraction of an extreme value distribution. We obtain explicit results for stopping values and approximative optimal stopping rules.
doi:10.1137/s0040585x97986011 fatcat:ermuadfmzzefroy5ki4jkw6tmq