Stability estimating in optimal stopping problem

Zaitseva, Elena

Kybernetika, Tome 44 (2008) no. 3, pp. 400-415.

Résumé

We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space $X$. It is supposed that an unknown transition probability $p(\cdot |x)$, $x\in X$, is approximated by the transition probability $\widetilde{p}(\cdot |x)$, $x\in X$, and the stopping rule $\widetilde{\tau }_*$, optimal for $\widetilde{p}$, is applied to the process governed by $p$. We found an upper bound for the difference between the total expected cost, resulting when applying $\widetilde{\tau }_*$, and the minimal total expected cost. The bound given is a constant times $\displaystyle \sup \nolimits _{x\in X}\Vert p(\cdot |x)-\widetilde{p}(\cdot |x)\Vert $, where $\Vert \cdot \Vert $ is the total variation norm.

Détail

Classification : 60G40, 60J10
Keywords: discrete-time Markov process; optimal stopping rule; stability index; total variation metric; contractive operator; optimal asset selling