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In this paper we introduce and solve a class of optimal stopping problems ofrecursive type. In particular, the stopping payoff depends directly on thevalue function of the problem itself. In a multi-dimensional Markovian settingwe show that the problem is well posed, in the sense that the value is indeedthe unique solution to a fixed point problem in a suitable space of continuousfunctions, and an optimal stopping time exists. We then apply our class ofproblems to a model for stock trading in two different market venues and wedetermine the optimal stopping rule in that case.

A class of recursive optimal stopping problems with applications to stock trading