# IJPAM: Volume 59, No. 3 (2010)

ROBUSTNESS ESTIMATING OF OPTIMAL STOPPING
PROBLEM WITH UNBOUNDED REVENUE
AND COST FUNCTIONS

Elena Zaitseva
Department of Mathematics
Instituto Tecnológico Autónomo de México
Rio Hondo # 124, Col. Tizapan San Angel
C.P. 01080, Mexico D.F., MEXICO
e-mail: elena.zaitseva@itam.mx

Abstract.We study the stability of the optimal stopping problem for a discrete-time Markov process on a general space state . Revenue and cost functions are allowed to be unbounded. The stability (robustness) is understood in the sense that an unknown transition probability , is approximated by the known one , , and the stopping rule optimal for the process governed by is applied to the original process represented by . The criteria of stopping rule optimization is the total expected return. We give an upper bound for the decrease of the return due to the replacement of the unknown optimal stopping rule by its approximation . The bound is expressed in terms of the weighted total variation distance between the transition probabilities and .