The system of quasi-variational inequalities attached to the two-armed bandit problem

Abstract

We give a characterization of the optimal value function of switching and stopping problems for two-parameter stochastic processes, particularly, bi-Markov processes in terms of the system of quasivariational inequalities, under the condition termed (F5) in Mazziotto and Millet [10]. We also give the construction of an optimal solution for such problems by the arguments of the one-parameter optimal stopping problem